Solve frac{sqrt{65}}{4}frac{sqrt{80}}{5}

$$\frac{ \sqrt{ 65 } }{ 4 } \frac{ \sqrt{ 80 } }{ 5 }$$

Evaluate

$$\sqrt{13}\approx 3.605551275$$

Solution Steps

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{\sqrt{65}}{4}\times \frac{4\sqrt{5}}{5}$$

Multiply \frac{\sqrt{65}}{4} times \frac{4\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{65}\times 4\sqrt{5}}{4\times 5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\sqrt{5}\sqrt{65}}{5}$$

Factor 65=5\times 13. Rewrite the square root of the product \sqrt{5\times 13} as the product of square roots \sqrt{5}\sqrt{13}.

$$\frac{\sqrt{5}\sqrt{5}\sqrt{13}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5\sqrt{13}}{5}$$

Cancel out 5 and 5.

$$\sqrt{13}$$