Q. 8.99 - Intermediate Algebra

Question

Simplify:

(a) $\frac{5}{\sqrt{3}}$

(b) $\sqrt{\frac{3}{32}}$

(c) $\frac{2}{\sqrt{2x}}$

Step-by-Step Solution

Answer

The simplification of $\frac{5}{\sqrt{3}}$ is $\frac{5\sqrt{3}}{3}$

The simplification of $\sqrt{\frac{3}{32}}$ is $\frac{\sqrt{6}}{8}$

The simplification of $\frac{2}{\sqrt{2x}}$ is $\frac{\sqrt{2x}}{x}$

Part (a) Step 1. Given

An expression $\frac{5}{\sqrt{3}}$

To simplify the expression 

Step 2. Multiply numerator and denominator by the same factor

Multiply numerator and denominator by $\sqrt{3}$

$\frac{5}{\sqrt{3}}=\frac{5\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$

        $=\frac{5\sqrt{3}}{3}$

Part (b) Step 1. Given

An expression $\sqrt{\frac{3}{32}}$

To simplify the expression 

Part (a) Step 2. Rewrite using the quotient property

The expression is not a perfect square, so rewrite using quotient property.

$\sqrt{\frac{3}{32}}=\frac{\sqrt{3}}{\sqrt{32}}$

          $=\frac{\sqrt{3}}{\sqrt{16}.\sqrt{2}}$

Step 3. Simplify the expression

$\sqrt{\frac{3}{32}}=\frac{\sqrt{3}}{4\sqrt{2}}$

Multiply numerator and denominator by $\sqrt{2}$,

          $=\frac{\sqrt{3}.\sqrt{2}}{4\sqrt{2}.\sqrt{2}}$

         $=\frac{\sqrt{6}}{8}$

The simplification of the expression is $\frac{\sqrt{6}}{8}$

Part (c) Step 1. Given

An expression  $\frac{2}{\sqrt{2x}}$

To simplify the expression

Part (c) Step 2. Multiply numerator and denominator by the same factor

Multiply the numerator and denominator by $\sqrt{2x}$

$\frac{2}{\sqrt{2x}}=\frac{2\sqrt{2x}}{\sqrt{2x}\sqrt{2x}}$

Simplify the expression

          $=\frac{2\sqrt{2x}}{2x}$

          $=\frac{\sqrt{2x}}{x}$

The simplification of the expression is $\frac{\sqrt{2x}}{x}$