Solve 3*sqrt{53*7%2}

$$3 \times \sqrt{ 53 \times 7 \% 2 }$$

Evaluate

$$\frac{3\sqrt{742}}{10}\approx 8.171903083$$

Solution Steps

Express 53\times \frac{7}{100} as a single fraction.

$$3\sqrt{\frac{53\times 7}{100}\times 2}$$

Multiply 53 and 7 to get 371.

$$3\sqrt{\frac{371}{100}\times 2}$$

Express \frac{371}{100}\times 2 as a single fraction.

$$3\sqrt{\frac{371\times 2}{100}}$$

Multiply 371 and 2 to get 742.

$$3\sqrt{\frac{742}{100}}$$

Reduce the fraction \frac{742}{100} to lowest terms by extracting and canceling out 2.

$$3\sqrt{\frac{371}{50}}$$

Rewrite the square root of the division \sqrt{\frac{371}{50}} as the division of square roots \frac{\sqrt{371}}{\sqrt{50}}.

$$3\times \frac{\sqrt{371}}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$3\times \frac{\sqrt{371}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{371}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$3\times \frac{\sqrt{371}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$3\times \frac{\sqrt{371}\sqrt{2}}{5\times 2}$$

To multiply \sqrt{371} and \sqrt{2}, multiply the numbers under the square root.

$$3\times \frac{\sqrt{742}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$3\times \frac{\sqrt{742}}{10}$$

Express 3\times \frac{\sqrt{742}}{10} as a single fraction.

$$\frac{3\sqrt{742}}{10}$$