Chapter 1.2, Problem 90E

(a)

To determine

To rationalize: the denominator of expression $\sqrt{\frac{5}{12}}$ .

Answer to Problem 90E

  $\sqrt{\frac{5}{12}}=\frac{\sqrt{15}}{6}$

Explanation of Solution

Given information:

Given expression

  $\sqrt{\frac{5}{12}}$

Calculation:

Consider the given expression.

  $\sqrt{\frac{5}{12}}$

Now, multiply the numerator and denominator by $\sqrt{12}$ .

  $\begin{array}{c}\sqrt{\frac{5}{12}}=\sqrt{\frac{5}{12}}\times \frac{\sqrt{12}}{\sqrt{12}}\\ =\frac{\sqrt{60}}{12}\\ =\frac{\sqrt{2\times 2\times 15}}{12}\\ =\frac{2\sqrt{15}}{12}\\ =\frac{\sqrt{15}}{6}\end{array}$

Hence,

  $\sqrt{\frac{5}{12}}=\frac{\sqrt{15}}{6}$

(b)

To determine

To rationalize: the denominator of expression $\sqrt{\frac{x}{6}}$ .

Answer to Problem 90E

  $\sqrt{\frac{x}{6}}=\frac{\sqrt{6x}}{6}$

Explanation of Solution

Given information:

Given expression

  $\sqrt{\frac{x}{6}}$

Calculation:

Consider the given expression.

  $\sqrt{\frac{x}{6}}$

Now, multiply the numerator and denominator by $\sqrt{6}$ .

  $\begin{array}{c}\sqrt{\frac{x}{6}}=\sqrt{\frac{x}{6}}\times \frac{\sqrt{6}}{\sqrt{6}}\\ =\frac{\sqrt{6x}}{6}\end{array}$

Hence,

(c)

To determine

To rationalize: the denominator of expression $\sqrt{\frac{y}{2z}}$ .

Answer to Problem 90E

  $\sqrt{\frac{y}{2z}}=\frac{\sqrt{2zy}}{2z}$

Explanation of Solution

Given information:

Given expression

  $\sqrt{\frac{y}{2z}}$

Calculation:

Consider the given expression.

  $\sqrt{\frac{y}{2z}}$

Now, multiply the numerator and denominator by $\sqrt{2z}$ .

  $\begin{array}{c}\sqrt{\frac{y}{2z}}=\sqrt{\frac{y}{2z}}\times \frac{\sqrt{2z}}{\sqrt{2z}}\\ =\frac{\sqrt{2zy}}{2z}\end{array}$

Hence,

  $\sqrt{\frac{y}{2z}}=\frac{\sqrt{2zy}}{2z}$