Chapter CSB, Problem 2.25E

To determine

To simplify: the given square root.

Answer to Problem 2.25E

  $\sqrt{\frac{81}{49}}=\frac{9}{7}$ .

Explanation of Solution

Given:

The given square rootis $\sqrt{\frac{81}{49}}$ .

Calculation:

As the given square root is $\sqrt{\frac{81}{49}}$ .

Now, to simplify the square root, therefore,

  $\begin{array}{l}\sqrt{\frac{81}{49}}=\sqrt{\frac{9\times 9}{7\times 7}}\left\{\text{factor of 81 and 49}\right\}\\ \sqrt{\frac{81}{49}}=\sqrt{\frac{9^2}{7^2}}\{\because \sqrt{a^2}=a\}\\ \therefore \sqrt{\frac{81}{49}}=\frac{9}{7}\end{array}$

Hence, the simplification of the given function is $\sqrt{\frac{81}{49}}=\frac{9}{7}$ .