Solve frac{sqrt{4}*sqrt{75}}{sqrt{3}}

$$\frac { \sqrt { 4 } \cdot \sqrt { 75 } } { \sqrt { 3 } }$$

Evaluate

$$10$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{2\sqrt{75}}{\sqrt{3}}$$

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}.

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

Multiply 2 and 5 to get 10.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply 10 and 3 to get 30.

$$\frac{30}{3}$$

Divide 30 by 3 to get 10.

$$10$$

Factor

$$2\times 5$$