Solve frac{3sqrt{2*50}}{sqrt{5}}

$$\frac{ 3 \sqrt{ 2 \times 50 } }{ \sqrt{ 5 } }$$

Evaluate

$$6\sqrt{5}\approx 13.416407865$$

Solution Steps

Multiply 2 and 50 to get 100.

$$\frac{3\sqrt{100}}{\sqrt{5}}$$

Calculate the square root of 100 and get 10.

$$\frac{3\times 10}{\sqrt{5}}$$

Multiply 3 and 10 to get 30.

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

Rationalize the denominator of \frac{30}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

Divide 30\sqrt{5} by 5 to get 6\sqrt{5}.

$$6\sqrt{5}$$