Solve frac{sqrt{4}*sqrt{75}}{sqrt{2}}

$$\frac { \sqrt { 4 } \cdot \sqrt { 75 } } { \sqrt { 2 } }$$

Evaluate

$$5\sqrt{6}\approx 12.247448714$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{2\sqrt{75}}{\sqrt{2}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

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

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{10\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{10\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{10\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{10\sqrt{6}}{2}$$

Divide 10\sqrt{6} by 2 to get 5\sqrt{6}.

$$5\sqrt{6}$$