Question

Find the square root of:

\[23\frac{26}{121}\]

Answer 1

 We know: 

\[\sqrt{2\frac{137}{196}} = \sqrt{\frac{529}{196}} = \frac{\sqrt{529}}{\sqrt{196}}\]

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

\[\sqrt{529} = \sqrt{23 \times 23} = 23\]
\[\sqrt{196} = \sqrt{2 \times 2 \times 7 \times 7} = 2 \times 7 = 14\]
\[ \therefore \sqrt{2\frac{137}{196}} = \frac{23}{14}\]