Chapter CSB, Problem 2.26E

To determine

To simplify: the given square root.

Answer to Problem 2.26E

  $\sqrt{\frac{25}{64}}=\frac{5}{8}$ .

Explanation of Solution

Given:

The given square rootis $\sqrt{\frac{25}{64}}$ .

Calculation:

As the given square root is $\sqrt{\frac{25}{64}}$ .

Now, to simplify the square root, therefore,

  $\begin{array}{l}\sqrt{\frac{25}{64}}=\sqrt{\frac{5\times 5}{8\times 8}}\left\{\text{factor of 25 and 64}\right\}\\ \sqrt{\frac{25}{64}}=\sqrt{\frac{5^2}{8^2}}\{\because \sqrt{a^2}=a\}\\ \therefore \sqrt{\frac{25}{64}}=\frac{5}{8}\end{array}$

Hence, the simplification of the given function is $\sqrt{\frac{25}{64}}=\frac{5}{8}$ .