Question

what is the exact value of the expressions the square root of 180. − the square root 125. the square root of 5.? simplify if possible.

Answer 1

$\sqrt{180}-\sqrt{125}\\\\\sqrt{180}=\sqrt{36\cdot5}=\sqrt{36}\cdot\sqrt5=6\sqrt5\\\sqrt{125}=\sqrt{25\cdot5}=\sqrt{25}\cdot\sqrt5=5\sqrt5\\\\\sqrt{180}-\sqrt{125}=6\sqrt5-5\sqrt5=(6-5)\sqrt5=\sqrt5$