Question

Determine the square root of 1296

Answer 1

$\sqrt{1296} = 36$

We may prove it if we know simplier square root values.

For example, we know that 2² = 4 and 1296 may be divided by 4(because its last 2 digits (96) may be divided by 4).

So, $\sqrt{1296} = \sqrt{\frac{1296}{4}} * \sqrt{4} = 2 * \sqrt{324}$

324 may also be divided by 4 (as its last 2 digits (24) may be divided by 4).

Thus, $2 * \sqrt{324} = 2* \sqrt{\frac{324}{4}} * \sqrt{4} = 4 * \sqrt{81}$

As we know, $\sqrt{81} = 9$ , so $\sqrt{1296} = 4 * 9 = 36$ .