Chapter 7.4, Problem 82PFA

To determine

To simplify the expression $\sqrt{2}\cdot \sqrt{22}$ .

Answer to Problem 82PFA

  $\sqrt{2}\cdot \sqrt{2}\cdot \sqrt{11}$

Explanation of Solution

Given:

  $\sqrt{2}\cdot \sqrt{22}$

Formula used:

The radical rules:

  $\sqrt[n]{a}=a^{\frac{1}{n}}$

  ${(a^m)}^n=a^{mn}$

  $\sqrt[a]{b\times c}=\sqrt[a]{b}\times \sqrt[a]{c}$

Calculation:

  $\begin{array}{l}\Rightarrow \sqrt{2}\cdot \sqrt{22}\\ \Rightarrow \sqrt{2}\cdot \sqrt{2\times 11}\\ \Rightarrow \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{11}[\because \sqrt[a]{b\times c}=\sqrt[a]{b}\times \sqrt[a]{c}]\\ \Rightarrow 2\sqrt{11}\end{array}$

Conclusion:

The simplified form of the given expression is equal to $\sqrt{2}\cdot \sqrt{2}\cdot \sqrt{11}.$