Question

What is the square root of 625

Answer 1

$De finition:\\\sqrt{a}=b\ \iff b^2=a\\=====================$

$625|5\\125|5\\.\ 25|5\\.\ \ 5|5\\.\ \ 1|\\\\625=5\times5\times5\times5=5^2\times5^2\\\\\sqrt{625}=\sqrt{5^2\times5^2}=(*)\\-------------------------------\\use:\ \sqrt{a\times b}=\sqrt{a}\times\sqrt{b}\ and\ \sqrt{a^2}=a\ for\ a\geq0\\-------------------------------\\(*)=\sqrt{5^2}\times\sqrt{5^2}=5\times5=\boxed{25}$

$Other\ solution:\\\\\sqrt{625}=25\ because\ 25^2=25\times25=625$