Chapter 11.6, Problem 1OE

To determine

To evaluate: the given expression.

Answer to Problem 1OE

  $\sqrt{6^2+8^2}=10$ .

Explanation of Solution

Given:

The given expression is $\sqrt{6^2+8^2}$ .

Calculation:

As the given expression is $\sqrt{6^2+8^2}$ .

Therefore,

  $\begin{array}{l}\sqrt{6^2+8^2}=\sqrt{6\times 6+8\times 8}\\ =\sqrt{36+64}\left\{\text{simplify}\right\}\\ =\sqrt{100}\left\{\text{addition}\right\}\\ =\sqrt{{10}^2}\\ \therefore \sqrt{6^2+8^2}=10\{\because \sqrt{a^2}=a\}\end{array}$

Hence, the simplified form of the given expression is $\sqrt{6^2+8^2}=10$ .