Q. 8.44 - Intermediate Algebra

Question

Simplify: $\sqrt{\frac{48x^5}{100}}.$

Step-by-Step Solution

Answer

After simplifying we get, $\frac{2x^2\sqrt{3x}}{5}.$

Step 1. Simplify the fraction in the radicand

Given: $\sqrt{\frac{48x^5}{100}}$ 

After simplifying the fraction in the radicand we can write as $\sqrt{\frac{12x^5}{25}}.$

Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Thus, we write $\sqrt{\frac{12x^5}{25}}$ as $\frac{\sqrt{12x^5}}{\sqrt{25}}.$

Step 3. Simplify the radicals of both the numerator and denominator

After simplifying we get,

$$\begin{gathered} \frac{\sqrt{12x^5}}{\sqrt{25}} \\ =\frac{\sqrt{{\left(2x^2\right)}^2}·\sqrt{3x}}{5} \\ =\frac{2x^2\sqrt{3x}}{5} \end{gathered}$$