Question

Is the square root of 81/676 irrational or rational?

Answer 1

The given square root is:

$\sqrt[]{\frac{81}{676}}$

Distribute the square root in the numerator and denominator of the fraction:

$\frac{\sqrt[]{81}}{\sqrt[]{676}}$

Both 81 and 676 are perfect squares, this means that their square root gives out a whole number as a result:

$\begin{gathered} \sqrt[]{81}=9 \\ \sqrt[]{676}=26 \end{gathered}$

Now the fraction is:

$\frac{9}{26}$

The result is 9/26 and you cannot simplify it any further, so:

The square root of 81/676 is a rational value.