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

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

Evaluate

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

Solution Steps

Factor 50=2\times 25. Rewrite the square root of the product \sqrt{2\times 25} as the product of square roots \sqrt{2}\sqrt{25}.

$$\frac{3\sqrt{2}\sqrt{2}\sqrt{25}}{\sqrt{5}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{3\times 2\sqrt{25}}{\sqrt{5}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{25}}{\sqrt{5}}$$

Calculate the square root of 25 and get 5.

$$\frac{6\times 5}{\sqrt{5}}$$

Multiply 6 and 5 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}.

$$6\sqrt{5}$$