Question

How to find the square root of $\frac{25}{12}$ to three decimal places.

Answer 1

We have

$\frac{25}{12}$

$=\sqrt{3\left(\frac{25}{36}\right)}$ [Multiplying 3 in numerator and denominator]

$=\sqrt{\left(\frac{25}{36}\right)}\cdot \sqrt{3}$ [$\because \sqrt{a\times b}=\sqrt{a}\times \sqrt{b}$]

$=\frac{5}{6}\times \sqrt{3}$ [$\because \sqrt{\left(\frac{25}{36}\right)}=\sqrt{\frac{5\times 5}{6\times 6}}=\frac{5}{6}$]

$=\frac{5\times \sqrt{3}}{6}$

$=\frac{8.66025}{6}$

$=1.443$