1
$\begingroup$

I'm stuck. Helping kid with alg II and the instructions say to simplify the expression into one radical. $$\sqrt{10} \cdot \sqrt[4]{3}$$ I know how to do it with same base, or same exponent, but ten to the 1/2 times 3 to the 1/4? Am I just overthinking this? I can't see it.

$\endgroup$
  • 1
    $\begingroup$ First step, $(\sqrt[4]{100})(\sqrt[4]{3})$. In general, if dealing with $x^{a/b}y^{c/d}$, first step is to bring $a/b$ and $c/d$ to a common denominator. $\endgroup$ – André Nicolas Dec 17 '15 at 20:21
0
$\begingroup$

Without the square root signs (in the other answers since deleted) it might be easier to see your way to the solution.

$$ 10^{\frac{1}{2}} 3^{\frac{1}{4}} = 10^{\frac{2}{4}} 3^{\frac{1}{4}} = (10^2 \times 3)^{\frac{1}{4}} = 300^{\frac{1}{4}} $$

This method will work for $x^ay^b$ when $a$ and $b$ are rational - just write the exponents using their least common denominator.

(I started this answer several hours ago before I saw @AndreNicolas comment.)

$\endgroup$
0
$\begingroup$

The trick is to realize that $\sqrt{10}$ can be rewritten as $\sqrt[4]{100}$. There are at least two ways to make this connection:

  • You could recognize that $10 = \sqrt{100}$, so $\sqrt{10}=\sqrt{\sqrt{100}}$.
  • You could write $\sqrt{10}$ as $10^{1/2}$, and then rewrite $1/2$ as $2/4$, so we have $10^{2/4} = (10^2)^{1/4}$.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.