Solve sqrt{16}sqrt{17/42}

$$\sqrt{ 16 } \sqrt{ 1 \frac{ 7 }{ 4 } 2 }$$

Evaluate

$$2\sqrt{22}\approx 9.38083152$$

Solution Steps

Calculate the square root of 16 and get 4.

$$4\sqrt{\frac{1\times 4+7}{4}\times 2}$$

Multiply 1 and 4 to get 4.

$$4\sqrt{\frac{4+7}{4}\times 2}$$

Add 4 and 7 to get 11.

$$4\sqrt{\frac{11}{4}\times 2}$$

Express \frac{11}{4}\times 2 as a single fraction.

$$4\sqrt{\frac{11\times 2}{4}}$$

Multiply 11 and 2 to get 22.

$$4\sqrt{\frac{22}{4}}$$

Reduce the fraction \frac{22}{4} to lowest terms by extracting and canceling out 2.

$$4\sqrt{\frac{11}{2}}$$

Rewrite the square root of the division \sqrt{\frac{11}{2}} as the division of square roots \frac{\sqrt{11}}{\sqrt{2}}.

$$4\times \frac{\sqrt{11}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{11}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{11}\sqrt{2}}{2}$$

To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{22}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{22}$$