Question

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

Answer 1

`\bf √(180)-√(125)+√(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} \\\\\\ √(6^2\cdot 5)-√(5^2\cdot 5)+√(5)\implies 6√(5)-5√(5)+√(5)\implies 2√(5)`