Solve {l}{sqrt{40}124}{*sqrt{1/5}}

$$\left. \begin{array} { l } { \sqrt { 40 } 124 } \\ { \times \sqrt { \frac { 1 } { 5 } } } \end{array} \right.$$

Evaluate

$$248\sqrt{2}\approx 350.724963469$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$124\times 2\sqrt{10}\sqrt{\frac{1}{5}}$$

Multiply 124 and 2 to get 248.

$$248\sqrt{10}\sqrt{\frac{1}{5}}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$248\sqrt{10}\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$248\sqrt{10}\times \frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$248\sqrt{10}\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$248\sqrt{10}\times \frac{\sqrt{5}}{5}$$

Express 248\times \frac{\sqrt{5}}{5} as a single fraction.

$$\frac{248\sqrt{5}}{5}\sqrt{10}$$

Express \frac{248\sqrt{5}}{5}\sqrt{10} as a single fraction.

$$\frac{248\sqrt{5}\sqrt{10}}{5}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\frac{248\sqrt{5}\sqrt{5}\sqrt{2}}{5}$$

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

$$\frac{248\times 5\sqrt{2}}{5}$$

Multiply 248 and 5 to get 1240.

$$\frac{1240\sqrt{2}}{5}$$

Divide 1240\sqrt{2} by 5 to get 248\sqrt{2}.

$$248\sqrt{2}$$