Solve sqrt{20}*sqrt{5}-frac{sqrt{75}}{sqrt{3}}

$$\sqrt{ 20 } \times \sqrt{ 5 } - \frac{ \sqrt{ 75 } }{ \sqrt{ 3 } }$$

Evaluate

$$5$$

Solution Steps

Factor 20=5\times 4. Rewrite the square root of the product \sqrt{5\times 4} as the product of square roots \sqrt{5}\sqrt{4}.

$$\sqrt{5}\sqrt{4}\sqrt{5}-\frac{\sqrt{75}}{\sqrt{3}}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5\sqrt{4}-\frac{\sqrt{75}}{\sqrt{3}}$$

Calculate the square root of 4 and get 2.

$$5\times 2-\frac{\sqrt{75}}{\sqrt{3}}$$

Multiply 5 and 2 to get 10.

$$10-\frac{\sqrt{75}}{\sqrt{3}}$$

Rewrite the division of square roots \frac{\sqrt{75}}{\sqrt{3}} as the square root of the division \sqrt{\frac{75}{3}} and perform the division.

$$10-\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$10-5$$

Subtract 5 from 10 to get 5.

$$5$$

Factor

$$5$$