Solve frac{5sqrt{15}}{5sqrt{48}}

$$\frac { 5 \sqrt { 15 } } { 5 \sqrt { 48 } }$$

Evaluate

$$\frac{\sqrt{5}}{4}\approx 0.559016994$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{\sqrt{15}}{\sqrt{48}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{\sqrt{15}}{4\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{15}}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{15}\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{15}\sqrt{3}}{4\times 3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}\sqrt{3}}{4\times 3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3\sqrt{5}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{3\sqrt{5}}{12}$$

Divide 3\sqrt{5} by 12 to get \frac{1}{4}\sqrt{5}.

$$\frac{1}{4}\sqrt{5}$$