Chapter A.10, Problem 22AYU

To determine

To find: Simplify the expression $\sqrt{5x}\sqrt{20x^3}$.

Answer to Problem 22AYU

The value of $\sqrt{5x}\sqrt{20x^3}=10x^2$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression $\sqrt{5x}\sqrt{20x^3}$.

Calculation:

If $n\ge 2$ is an integer and a is a real number, then

$\sqrt[n]{a^n}=a$ if $n\ge 3$ is odd.

$\sqrt[n]{a^n}=\left|a\right|$ if $n\ge 2$ is even.

$\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

$\sqrt{5x}\sqrt{20x^3}=\sqrt{5\times x}\sqrt{5\times 4\times x^2\times x}=\sqrt{5\times x}\sqrt{5\times 2^2\times x^2\times x}$

$\sqrt{5\times x}\sqrt{5\times 2^2\times x^2\times x}=\sqrt{5}\times \sqrt{x}\times \sqrt{5}\times \sqrt{2^2}\times \sqrt{x^2}\times \sqrt{x}=\sqrt{5}\times \sqrt{x}\times \sqrt{5}\times \left|2\right|\times \left|x\right|\times \sqrt{x}=5\times x\times 2\times x=10x^2$