Chapter A.10, Problem 39AYU

To determine

To find: Simplify the expression $\sqrt{8x^3}-3\sqrt{50x}$.

Answer to Problem 39AYU

The value of $\sqrt{8x^3}-3\sqrt{50x}=\sqrt{2x}\left(2x-15\right)$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression $\sqrt{8x^3}-3\sqrt{50x}$.

Calculation:

Consider $\sqrt{8x^3}-3\sqrt{50x}$,

$\sqrt{8x^3}-3\sqrt{50x}=\sqrt{4\times 2\times x^2\times x}-3\sqrt{25\times 2\times x}$

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

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

$=\sqrt{2x}\left(\left|2\right|\times \left|x\right|-3\times \left|5\right|\right)$

$=\sqrt{2x}\left(2x-15\right)$