Solve 5frac{sqrt{15}}{2sqrt{30}}

$$5 \frac{ \sqrt{ 15 } }{ 2 \sqrt{ 30 } }$$

Evaluate

$$\frac{5\sqrt{2}}{4}\approx 1.767766953$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{15}}{2\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$5\times \frac{\sqrt{15}\sqrt{30}}{2\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$5\times \frac{\sqrt{15}\sqrt{30}}{2\times 30}$$

Factor 30=15\times 2. Rewrite the square root of the product \sqrt{15\times 2} as the product of square roots \sqrt{15}\sqrt{2}.

$$5\times \frac{\sqrt{15}\sqrt{15}\sqrt{2}}{2\times 30}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$5\times \frac{15\sqrt{2}}{2\times 30}$$

Multiply 2 and 30 to get 60.

$$5\times \frac{15\sqrt{2}}{60}$$

Divide 15\sqrt{2} by 60 to get \frac{1}{4}\sqrt{2}.

$$5\times \frac{1}{4}\sqrt{2}$$

Multiply 5 and \frac{1}{4} to get \frac{5}{4}.

$$\frac{5}{4}\sqrt{2}$$