3
votes
1answer
37 views

Simplify $\frac {\sqrt5}{\sqrt3+1} - \sqrt\frac{30}{8} + \frac {\sqrt {45}}{2}$

I am trying to find the value of: $$\frac {\sqrt5}{\sqrt3+1} - \sqrt\frac{30}{8} + \frac {\sqrt {45}}{2}$$ I have the key with the answer $\sqrt 5$ but am wondering how I can easily get to that ...
4
votes
2answers
70 views

How prove that $ \sqrt[3]{\frac{1}{9}}+\sqrt[3]{-\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}=\sqrt[3]{\sqrt[3]2-1} $

How check that $ \sqrt[3]{\frac{1}{9}}+\sqrt[3]{-\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}=\sqrt[3]{\sqrt[3]2-1} $?
0
votes
1answer
40 views

Simplifying Surd Fractions

can someone show me how to simple surd fractions such as: $$\frac{{8\sqrt 3 }}{2}$$ Can someone please help me here?
2
votes
3answers
163 views

How can this equality be established by elementary algebraic means?

Let $x \geq 1$. Then is it true that $2x^3 - 3x^2 + 2 \geq 1$? If so, how can I show this using only elementary ideas such as factorisation? Of course, I can demonstrate this using the methods of ...
4
votes
2answers
59 views

How to turn arbitrary fractions into arbitrary egyptian fractions?

I am reading Stillwell's Numbers and Geometry. There is an exercise about Egyptian fractions which is the following: I've tried to do it in the following way - Expressing an arbitrary fraction ...
0
votes
3answers
44 views

When a fraction is raised to a negative exponent, do you normally transform it to 1 over the fraction, or invert the fraction?

My text shows that $$\left(\frac{3a^2}{4b}\right)^{-3}=\frac{1}{\left(\frac{3a^2}{4b}\right)^{3}}.$$ It also shows that $$\frac{1}{\frac{144}{b}}=\frac{b}{144}.$$ In the first equation, it seems ...
1
vote
2answers
78 views

Why does $(3^{1/2})(10^{1/2})=30^{1/2}$ but $(3a^2)(10a^2)=30a^4$?

$(3a^2)(10a^2)=30a^4$? In that equation the exponents are added. Why does $(3^{1/2})(10^{1/2})=30^{1/2}$. In that equation the exponents are not added. Why?
2
votes
2answers
42 views

Square root each term (clarification on polynomials?)

So I'm in Algebra 2, and right now we're learning about conic sections (circles/ellipse/etc). I thought some problems in the workbook looked weird, like this one: ...
2
votes
3answers
51 views

Square root of a squared number changes sign, which to apply first?

Heres something Ive always found interesting. Supose we have a variable $x$, and $x$ equals a negative number: Say: $$x=-17$$ Now, I can apply a square to both sides of the equation and preserve ...
0
votes
1answer
40 views

How to derive this formula about the bracket function?

Is there a direct way of proving that $$ [nx] = [x] + [x+\frac{1}{2}] + [x+\frac{1}{3}] + \ldots + [x+ \frac{1}{n}]$$ for each real number $x$ and for each positive integer $n$? My effort: Let ...
0
votes
2answers
25 views

Quarters weigh 6 grams while dimes weigh 2 grams.

Quarters weigh $6$ grams while dimes weigh $2$ grams. Tiffany has $\$5.35$ worth of quarters and dimes in her pocket weighing a total of $124$ grams. How many quarters does Tiffany have?
2
votes
1answer
93 views

How to find the integer part of big number?

How to calculate the integer part $$\left \lfloor10^{10^{10^{10^{10^{-10^{10}}}}}} \right \rfloor ?$$ Does this equal $$10^{10^{10}}? $$ Both Maple and Mathematica fail with it. PS. Unmotivated votes ...
1
vote
3answers
41 views

How to establish these two facts about polynomials?

Let $f(x) := \sum_{k=0}^n c_k x^k $ be a polynomial of degree $n\geq 0$ with real coefficeints such that $f(x) = 0$ for $n+1$ distinct real values of $x$. Then how to prove that each $c_k = 0$ and ...
3
votes
8answers
351 views

$\left(\sqrt{8}+\sqrt{2}\right)^2$ = 18 why??

I would like to now why $$\left(\sqrt{8}+\sqrt{2}\right)^2$$ is equal to $18$? Please provide me the proccess. Thank you.
0
votes
1answer
13 views

Really Simple Re Weighting Question

I am having a major brain cramp and cannot remember how to to this. In a perfect world I have 7 types of activities that I could have participated in. These 7 activities each have a weight that ...
0
votes
2answers
64 views

A man invests an amount of $ ₹ 15860 $ in the names of his three sons A, B & C in such a way that they get the same interest..

A man invests an amount of $ ₹ 15860 $ in the names of his three sons A, B & C in such a way that they get the same interest after $2, 3$ & $4$ years respectively. If the rate of simple ...
6
votes
5answers
175 views

Simple solving Skanavi book exercise: $\sqrt[3]{9+\sqrt{80}}+\sqrt[3]{9-\sqrt{80}}$

Simple way to solve this exercise $$ x = \sqrt[3]{9+\sqrt{80}}+\sqrt[3]{9-\sqrt{80}} $$
1
vote
3answers
61 views

Given a rational, how to find the integers whose quotient it is?

I haven't found an answer to this anywhere. Excluding brute force, given a rational $q$ in its decimal form ($1.47$, for example), is there a good algorithm to find integers $m$ and $n$ such that ...
5
votes
1answer
53 views

Halmos on Definability and Luzin on Division by 0

For a successful introduction of a new symbol (e.g. '$\emptyset$') into a mathematical discourse it is necessary and sufficient that the symbol refer to something (e.g. Existence + Specification in ...
0
votes
2answers
39 views

How do you get from this to this formula?

I have the formula : $$3×4^{n-1}×1×\left({1\over 3}\right)^{n-1}$$ And I would like to know how to get to this one (which is equal) : $$3× \left({4\over 3}\right)^{n-1}$$ How can I do that ?
1
vote
3answers
51 views

Inequality involving conjugate numerator/denominator pairs

Question is to solve: $$\frac{(x-2)(x-4)(x-7)}{(x+2)(x+4)(x+7)} > 1$$ I thought I could negate terms to make them equal (i.e. $-(x-2)$), but that does not happen. I could subtract $1$ from ...
2
votes
3answers
44 views

Solving this inequality

Question: Solve: $$\frac{5x-6}{x+6}<1$$ My attempt: $$\frac{5x-6-x-6}{x+6}<0$$ $$\Rightarrow \frac{4x-12}{x+6}<0$$ $$\Rightarrow \frac{x-3}{x+6}<0$$ $$\Rightarrow (x-3)(x+6) < ...
1
vote
2answers
56 views

Isn't this wrong?

This worksheet This question: $$w^2 - w \leq 0$$ This answer: $$(-\infty, -1] \cup [0, 1]$$ Isn't this wrong ? At $w = -2$, it becomes: $(-2)^2 - (-2)$, which is $4 + 2$, which is $\geq 0$. But ...
1
vote
3answers
41 views

How to solve this inequality question without manual checking?

Question: Find the maximum integral value which satisfies: $$\frac{x-2}{x^2-9}<0$$ I know that this means either of the following: #1. $x-2<0$ and $x^2-9>0$. Implies that $x \in (3, ...
3
votes
3answers
227 views

Which is greater: $1000^{1000}$ or $1001^{999}$

Question: Find the greater number: $1000^{1000}$ or $1001^{999}$ My Attempt: I know that: $(a+b)^n \geq a^n + a^{n-1}bn$. Thus, $(1+999)^{1000} \geq 999001$ And $(1+1000)^{999} \geq ...
0
votes
2answers
32 views

Solving two systems with two unknown?

Let's say if we are giving the following two equations: $$ 1= X/(X^2 +Y^2) $$ $$ 2= Y/(X^2 +Y^2) $$ How are we going to solve for X and Y [ by HAND ] ? Why would Summing the squares of the two ...
1
vote
1answer
18 views

Comparing powers with different bases without logarithms

I want to compare : $17^{31}$ and $31^{17}$ , this is a solution but I want another one and without using logarithms, only using the fact that $17=16+1=(2^4)+1$ and $31=(2^5)-1$ how could it ...
-4
votes
2answers
49 views

PEMDAS: Why do I get different values when “trying” to use PEMDAS? [closed]

The real question is why is $(2 + 2)^2 = 16$ and $(a + b)^2 = (a + b) (a + b)$?
1
vote
0answers
25 views

Arithmetic and Algebra exercises on latex source code.

I´m currently writing a little book for two student that I teach. The book covers school arithmetics and algebra, and it include theory and examples. Since I don´t have time to prepare a good sets of ...
0
votes
1answer
29 views

What expression represents the total cost?

A customer calculated the cost of a new jacket , c, including a 7% sales tax, by multiplying 0.07 times the cost of the jacket and adding the product to the cost of the jacket. What is another way to ...
1
vote
5answers
164 views

Algebra problem stumping me

I have recently run into an algebra problem that goes as follows. Using the digits $1$ to $9$, $$ \left\{ \begin{align} A + B + C + D &= EF \\ E + F + G + H &= CJ \\ B + G + J ...
2
votes
1answer
48 views

Formula for this pattern

I am trying to develop a computer program to compute the tax for a given base salary, I believe given the format of the income tax table that I have there should be a formula to calculate the tax for ...
1
vote
1answer
54 views

Why ${(a^2)}^{\frac 12}=\sqrt {a^2}=|a| \neq a$?

Let $a\in \mathbb R$. It should be true that $\sqrt {a^2}=|a|$, since $\sqrt {(-2)^2}=\sqrt{2^2}=2$ and so on. But, it is also true that ${(a^2)}^{\frac 12}=a$, and by definition, ${(a^2)}^{\frac ...
0
votes
4answers
75 views

A seemingly basic PEMDAS problem… [duplicate]

There's one of those meme-type images posted on Facebook with the equation 6/2(1+2), challenging you to solve it. So, parenthesis first, ...
4
votes
1answer
80 views

Calculate the summation of double continued fractions

A few month ago, my brother had given me this question: \begin{equation} \cfrac{1}{2 + \cfrac{1}{3 + \cfrac{1}{4 + \cfrac{1}{\cdots+\frac{1}{2005}} } } }+\cfrac{1}{1 + ...
0
votes
2answers
81 views

What does this equal? $6\div 2(1+2)$

How do you figure out what $$6\div 2(2+1)$$ is equal? I get $9$, but some people say $7$ or even $1$ and I don't know how they get that? What does it really equal?
0
votes
1answer
50 views

Is there a term for this subtraction formula?

Is there a term for this concept? Any link? n is a decimal from 0 to 1, including FORMULA n = 0.5 x = 1 - n EXAMPLES ...
0
votes
1answer
31 views

How to prove that both of them are the same?

$$ 3^{n+1}-2^{n+1} = \left [ 38\cdot 2^{n-3}+ \sum_{i=3}^{n}\left ( 2^{n-i}\cdot 3^{i} \right ) \right ],n\geq 3 $$ I had a college entrance exam few days ago, and I checked my answer with others. ...
1
vote
1answer
49 views

I need to do math from ground up, so what is a good workbook?

Can you guys recommend me a workbook that begins with arithmetic and ends with calculus. Or from pre-algebra to calculus. Like all "Master Math Series" books but in one complete book. It would really ...
0
votes
3answers
80 views

How do I simplify $\frac{\sqrt{4+h}-2}{h}$? [duplicate]

I know this looks like a dumb question, but how do I simplify this? Does it uses some square root property or factorization? The wolfram alpha has no step-by-step solution for this, so it may use some ...
-1
votes
2answers
49 views

If all 7's are replaced by the digit 6 , then the number of 6's in series 1,2,3,4…99, 100 will be (options)

As the title says. The options available are: (A) 31 (B) 32 (C) 33 (D) none of these Thanks in advance. :)
1
vote
4answers
58 views

Cancelling out square roots gives 2?

Question: If $$N = \frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}$$Find N (This is a subset of a larger question) My approach: After rationalizing the denominator, by ...
5
votes
4answers
265 views

Rational numbers - rationalization

Question: $$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$$ equals: My approach: I tried to rationalize the denominator by multiplying it by ...
6
votes
2answers
85 views

Is $\frac{0}{0}$ different from $\frac{1}{0}$?

In my mind, zero divided by zero answers the question of what $a$, when multiplied with zero, equals zero: $a * 0 = 0$ Obviously, any real number will satisfy this equation. However, one divided by ...
3
votes
4answers
192 views

Why does $\sqrt{x^2}=|x|$? [duplicate]

By convention, we say that: $$\sqrt{x^2}=|x|$$ In fact, the above statement is how we define absolute value. We would not write $\sqrt{4}=-2$. Although logically it is correct, by convention it is ...
1
vote
2answers
55 views

What is the name for finding biggest two multipliers of a number?

Excuse my English please. I am looking for the name in Mathematics (/English) for finding the biggest two numbers that form an array that can contain at minimum ...
0
votes
2answers
83 views

simplify $3x^2 \times x^2 + x^3 \times 2x$

Looking at an old assignment, and the function in the title is a derivative result of the product rule, but I've simplified it to $5x^4$, but I have forgotten how I got to that result. Anyone with a ...
0
votes
1answer
22 views

What percentage is the rest of the black cars in the parking lot

Ok so, Last Monday, a parking lot had 80 cars. Of those 80 cars, 25% were silver. 16 were red, and the rest were black. What percent of the cars were black
0
votes
3answers
90 views

negative exponent confusion

I am a bit confused with negative exponents so here is an example. Let $4$ to the $-3 = 1\div4\div4\div4 $ The thing which confuses me is the $1$, why we use $1$ before dividing. so if i do it ...
-6
votes
1answer
50 views

Postal work math [closed]

If you have 11 pieces and they weigh 6.8 oz. Together What is the individual weight of each piece and ur answer has to be in decimal form of a pound , such as, 0._ _ _ _ lb per piece