Chapter 9.1, Problem 3PSA

a

To determine

To simplify: The Value of $\frac{1}{\sqrt{2}}$ .

Answer to Problem 3PSA

The Values of $\frac{1}{\sqrt{2}}$ is $\frac{\sqrt{2}}{2}$ .

Explanation of Solution

Given information:$\frac{1}{\sqrt{2}}$

Formula used: $\sqrt{a}\times \sqrt{a}=a$

Calculation: $\frac{1}{\sqrt{2}}$

Rationalizing the denominator,

  $\begin{array}{l}\Rightarrow \frac{1}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}\\ \Rightarrow \frac{\sqrt{2}}{\sqrt{2}\times \sqrt{2}}\\ \Rightarrow \frac{\sqrt{2}}{2}\end{array}$

b

To determine

To simplify: The Value of $\frac{1}{\sqrt{5}}$ .

Answer to Problem 3PSA

The Values of $\frac{1}{\sqrt{5}}$ is $\frac{\sqrt{5}}{5}$ .

Explanation of Solution

Given information:$\frac{1}{\sqrt{5}}$

Formula used: $\sqrt{a}\times \sqrt{a}=a$

Calculation: $\frac{1}{\sqrt{5}}$

Rationalizing the denominator,

  $\begin{array}{l}\Rightarrow \frac{1}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}\\ \Rightarrow \frac{\sqrt{5}}{\sqrt{5}\times \sqrt{5}}\\ \Rightarrow \frac{\sqrt{5}}{5}\end{array}$

c

To determine

To simplify: The Value of $\frac{4}{\sqrt{2}}$ .

Answer to Problem 3PSA

The Values of $\frac{4}{\sqrt{2}}$ is $2\sqrt{2}$ .

Explanation of Solution

Given information:$\frac{4}{\sqrt{2}}$

Formula used: $\sqrt{a}\times \sqrt{a}=a$

Calculation: $\frac{4}{\sqrt{2}}$

Rationalizing the denominator,

  $\begin{array}{l}\Rightarrow \frac{4}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}\\ \Rightarrow \frac{4\sqrt{2}}{\sqrt{2}\times \sqrt{2}}\\ \Rightarrow \frac{4\sqrt{2}}{2}\\ \Rightarrow 2\sqrt{2}\end{array}$

d

To determine

To simplify: The Value of $\frac{6}{\sqrt{3}}$ .

Answer to Problem 3PSA

Values of $\frac{6}{\sqrt{3}}$ is $2\sqrt{3}$ .

Explanation of Solution

Given information:$\frac{6}{\sqrt{3}}$

Formula used: $\sqrt{a}\times \sqrt{a}=a$

Calculation: $\frac{6}{\sqrt{3}}$

Rationalizing the denominator,

  $\begin{array}{l}\Rightarrow \frac{6}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}\\ \Rightarrow \frac{6\sqrt{3}}{\sqrt{3}\times \sqrt{3}}\\ \Rightarrow \frac{6\sqrt{3}}{3}\\ \Rightarrow 2\sqrt{3}\end{array}$