Chapter SH, Problem 6.15EP

To determine

Find the simplified form of the given expression.

Answer to Problem 6.15EP

The simplified form of the expression is $6+3\sqrt{2}$ .

Explanation of Solution

Given:

The given expression is $\sqrt{36}+2\sqrt{32}-\sqrt{50}$ .

Calculation:

Rewrite the given expression.

  $\sqrt{6^2}+2\sqrt{2\cdot 16}-\sqrt{2\cdot 25}$

Applyradicalproperty $\sqrt[n]{xy}=\sqrt[n]{x}\sqrt[n]{y}$ .

  $\begin{array}{l}=\sqrt{6^2}+2\sqrt{2}\cdot \sqrt{16}-\sqrt{2}\cdot \sqrt{25}\\ =\sqrt{6^2}+2\sqrt{2}\cdot \sqrt{4^2}-\sqrt{2}\cdot \sqrt{5^2}\end{array}$

Apply radical property $\sqrt[n]{x^n}=x,x\ge 0$ .

  $\begin{array}{l}=6+2\sqrt{2}\cdot 4-\sqrt{2}\cdot 5\\ =6+8\sqrt{2}-5\sqrt{2}\end{array}$

Combine like terms.

  $=6+3\sqrt{2}$

Hence the simplified form of the expression is $6+3\sqrt{2}$ .