Question

1. Simplify the expression. Show your work.

Answer 1

$\sqrt{\frac{4 x^{2}}{3 y}}=\frac{2x }{\sqrt{3y} }$

Solution:

Given expression:

$\sqrt{\frac{4 x^{2}}{3 y}}$

To simplify the given expression:

4 can be written as 2 × 2 = 2²

x can be written as x × x = x²

$\sqrt{\frac{4 x^{2}}{3 y}}=\sqrt{\frac{2^2 x^{2}}{3 y}}$

         $=\sqrt{\frac{(2 x)^{2}}{3 y}}$

Using radical rule: $\sqrt{\frac{a^m}{b^m} } =\frac{ \sqrt{a^m} }{ \sqrt{b^n} }$

         $=\frac{\sqrt{(2x)^2} }{\sqrt{3y} }$

In numerator square and square root get cancelled.

         $=\frac{2x }{\sqrt{3y} }$

$\sqrt{\frac{4 x^{2}}{3 y}}=\frac{2x }{\sqrt{3y} }$

Hence the expression is simplified.