Question

What is the exact of the expressions square root of 180 - square root of 125 + square root of 5

Answer 1

$\bf \sqrt{180}-\sqrt{125}+\sqrt{5}\qquad \begin{cases} 180=2\cdot 2\cdot 3\cdot 3\cdot 5\\ \qquad 2^2\cdot 3^2\cdot 5\\ \qquad (2\cdot 3)^2\cdot 5\\ \qquad 6^2\cdot 5\\ 125=5\cdot 5\cdot 5\\ \qquad 5^2\cdot 5 \end{cases} \\\\\\ \sqrt{6^2\cdot 5}-\sqrt{5^2\cdot 5}+\sqrt{5}\implies 6\sqrt{5}-5\sqrt{5}+\sqrt{5}\implies 2\sqrt{5}$