Solve sqrt{1/sqrt{100-19}+16/sqrt{36}*frac{sqrt{100-64}}{3}}

$$\sqrt { \frac { 1 } { \sqrt { 100 - 19 } } + \frac { 16 } { \sqrt { 36 } } \cdot \frac { \sqrt { 100 - 64 } } { 3 } }$$

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

Subtract 19 from 100 to get 81.

$$\sqrt{\frac{1}{\sqrt{81}}+\frac{16}{\sqrt{36}}\times \frac{\sqrt{100-64}}{3}}$$

Calculate the square root of 81 and get 9.

$$\sqrt{\frac{1}{9}+\frac{16}{\sqrt{36}}\times \frac{\sqrt{100-64}}{3}}$$

Calculate the square root of 36 and get 6.

$$\sqrt{\frac{1}{9}+\frac{16}{6}\times \frac{\sqrt{100-64}}{3}}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{9}+\frac{8}{3}\times \frac{\sqrt{100-64}}{3}}$$

Subtract 64 from 100 to get 36.

$$\sqrt{\frac{1}{9}+\frac{8}{3}\times \frac{\sqrt{36}}{3}}$$

Calculate the square root of 36 and get 6.

$$\sqrt{\frac{1}{9}+\frac{8}{3}\times \frac{6}{3}}$$

Divide 6 by 3 to get 2.

$$\sqrt{\frac{1}{9}+\frac{8}{3}\times 2}$$

Express \frac{8}{3}\times 2 as a single fraction.

$$\sqrt{\frac{1}{9}+\frac{8\times 2}{3}}$$

Multiply 8 and 2 to get 16.

$$\sqrt{\frac{1}{9}+\frac{16}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{1}{9} and \frac{16}{3} to fractions with denominator 9.

$$\sqrt{\frac{1}{9}+\frac{48}{9}}$$

Since \frac{1}{9} and \frac{48}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1+48}{9}}$$

Add 1 and 48 to get 49.

$$\sqrt{\frac{49}{9}}$$

Rewrite the square root of the division \frac{49}{9} as the division of square roots \frac{\sqrt{49}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$