Question

Compute $\sqrt{25^2-7^2}$.

Answer 1

24

Explanation:

First we compute the number under the radical.

We have 25² = 625 and 7² = 49, so 25² - 7² = 625 - 49 = 576.

Thus, √25² - 7² = √576 = √24², which is 24.

Answer 2

24

Explanation:

`√(25^2-7^2)\\\\=√((25-7)(25+7))\\\\=√(18(32))\\\\=√(9*2*2^5)\\\\=√(3^2\cdot 2^6)\\\\=√((3\cdot2^3)^2)\\\\=3\cdot2^3\\\\=3\cdot8\\\\=24`