Chapter CSB, Problem 2.31E

To determine

To simplify: the given square root.

Answer to Problem 2.31E

  $\sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}=0.81$ .

Explanation of Solution

Given:

The given square rootis $\sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}$ .

Calculation:

As the given square root is $\sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}$ .

Now, to simplify the square root, therefore,

  $\begin{array}{l}\sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}=\sqrt{\frac{2\times 7}{7\times 3}}\left\{\because \sqrt{\frac{a}{b}}\cdot \sqrt{\frac{c}{d}}=\sqrt{\frac{a\times c}{b\times d}}\right\}\\ \sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}=\sqrt{\frac{2}{3}}\{\text{simplify}}\\ \sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}=\sqrt{0.667}\\ \therefore \sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}=0.81\end{array}$

Hence, the simplification of the given function is $\sqrt{\frac{2}{7}}\cdot \sqrt{\frac{7}{3}}=0.81$ .