Question

Find the square root of:

\[\frac{441}{961}\] 

Answer 1

We know: 

\[\sqrt{\frac{441}{961}} = \frac{\sqrt{441}}{\sqrt{961}}\]

Now, let us compute the square roots of the numerator and the denominator separately.

\[\sqrt{441} = \sqrt{\left( 3 \times 3 \right) \times \left( 7 \times 7 \right)} = 3 \times 7 = 21\]
\[\sqrt{961} = \sqrt{31 \times 31} = 31\]
\[ \therefore \sqrt{\frac{441}{961}} = \frac{21}{31}\]