Solve sqrt{16}sqrt{1+7/4+2}

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

Evaluate

$$2\sqrt{19}\approx 8.717797887$$

Solution Steps

Calculate the square root of 16 and get 4.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{4}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

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

Add 4 and 7 to get 11.

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

Convert 2 to fraction \frac{8}{4}.

$$4\sqrt{\frac{11}{4}+\frac{8}{4}}$$

Since \frac{11}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$4\sqrt{\frac{11+8}{4}}$$

Add 11 and 8 to get 19.

$$4\sqrt{\frac{19}{4}}$$

Rewrite the square root of the division \sqrt{\frac{19}{4}} as the division of square roots \frac{\sqrt{19}}{\sqrt{4}}.

$$4\times \frac{\sqrt{19}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$4\times \frac{\sqrt{19}}{2}$$

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

$$2\sqrt{19}$$