Solve 44*sqrt{5+1/16}

$$44 \times \sqrt { 5 + \frac { 1 } { 16 } }$$

Evaluate

$$99$$

Solution Steps

Convert 5 to fraction \frac{80}{16}.

$$44\sqrt{\frac{80}{16}+\frac{1}{16}}$$

Since \frac{80}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$44\sqrt{\frac{80+1}{16}}$$

Add 80 and 1 to get 81.

$$44\sqrt{\frac{81}{16}}$$

Rewrite the square root of the division \frac{81}{16} as the division of square roots \frac{\sqrt{81}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$44\times \frac{9}{4}$$

Express 44\times \frac{9}{4} as a single fraction.

$$\frac{44\times 9}{4}$$

Multiply 44 and 9 to get 396.

$$\frac{396}{4}$$

Divide 396 by 4 to get 99.

$$99$$

Factor

$$3^{2}\times 11$$