Solve (sqrt{4/9}+sqrt{16/25}-sqrt{1/225})^2=

$$( \sqrt { \frac { 4 } { 9 } } + \sqrt { \frac { 16 } { 25 } } - \sqrt { \frac { 1 } { 225 } } ) ^ { 2 } =$$

Evaluate

$$\frac{49}{25}=1.96$$

Solution Steps

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\left(\frac{2}{3}+\sqrt{\frac{16}{25}}-\sqrt{\frac{1}{225}}\right)^{2}$$

Rewrite the square root of the division \frac{16}{25} as the division of square roots \frac{\sqrt{16}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\left(\frac{2}{3}+\frac{4}{5}-\sqrt{\frac{1}{225}}\right)^{2}$$

Add \frac{2}{3} and \frac{4}{5} to get \frac{22}{15}.

$$\left(\frac{22}{15}-\sqrt{\frac{1}{225}}\right)^{2}$$

Rewrite the square root of the division \frac{1}{225} as the division of square roots \frac{\sqrt{1}}{\sqrt{225}}. Take the square root of both numerator and denominator.

$$\left(\frac{22}{15}-\frac{1}{15}\right)^{2}$$

Subtract \frac{1}{15} from \frac{22}{15} to get \frac{7}{5}.

$$\left(\frac{7}{5}\right)^{2}$$

Calculate \frac{7}{5} to the power of 2 and get \frac{49}{25}.

$$\frac{49}{25}$$

Factor

$$\frac{7 ^ {2}}{5 ^ {2}} = 1\frac{24}{25} = 1.96$$