√60 divided by 2√5

Answer 1

To simplify the expression \(\frac{\sqrt{60}}{2\sqrt{5}}\), we can follow these steps:

1. Simplify \(\sqrt{60}\): \[ \sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15} \]

2. Substitute this back into the expression: \[ \frac{\sqrt{60}}{2\sqrt{5}} = \frac{2\sqrt{15}}{2\sqrt{5}} \]

3. Cancel the \(2\) in the numerator and denominator: \[ \frac{2\sqrt{15}}{2\sqrt{5}} = \frac{\sqrt{15}}{\sqrt{5}} \]

4. Simplify \(\frac{\sqrt{15}}{\sqrt{5}}\): \[ \frac{\sqrt{15}}{\sqrt{5}} = \sqrt{\frac{15}{5}} = \sqrt{3} \]

So, the final result is: \[ \frac{\sqrt{60}}{2\sqrt{5}} = \sqrt{3} \]