# Tagged Questions

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### 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 ...
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### 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 $\sqrt[3]{\frac{1}{9}}+\sqrt[3]{-\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}=\sqrt[3]{\sqrt[3]2-1}$?
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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: ...
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### 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 ...
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### 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 ...
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### 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, ...
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### Calculate the summation of double continued fractions

A few month ago, my brother had given me this question: \cfrac{1}{2 + \cfrac{1}{3 + \cfrac{1}{4 + \cfrac{1}{\cdots+\frac{1}{2005}} } } }+\cfrac{1}{1 + ...
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### 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?
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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. :)
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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
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 ...