Find the value of each expression

Question

Square root of 45 - square root of 20 + square root of 5

Answer 1

To simplify the expression \(\sqrt{45} - \sqrt{20} + \sqrt{5}\), let's break down each square root into simpler components:

1. Calculate \(\sqrt{45}\): \[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \]

2. Calculate \(\sqrt{20}\): \[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} \]

Now substituting these simplifications back into the expression:

\[ \sqrt{45} - \sqrt{20} + \sqrt{5} = 3\sqrt{5} - 2\sqrt{5} + \sqrt{5} \]

Next, we combine the terms involving \(\sqrt{5}\):

\[ (3\sqrt{5} - 2\sqrt{5} + \sqrt{5}) = (3 - 2 + 1)\sqrt{5} = 2\sqrt{5} \]

Thus, the final value of the expression \(\sqrt{45} - \sqrt{20} + \sqrt{5}\) is:

\[ \boxed{2\sqrt{5}} \]