Solve (2/3)^-2+5^2(-1/5+2/5)^2+sqrt{9/4}

$$( \frac { 2 } { 3 } ) ^ { - 2 } + 5 ^ { 2 } ( \frac { - 1 } { 5 } + \frac { 2 } { 5 } ) ^ { 2 } + \sqrt { \frac { 9 } { 4 } }$$

Evaluate

$$\frac{19}{4}=4.75$$

Solution Steps

Calculate \frac{2}{3} to the power of -2 and get \frac{9}{4}.

$$\frac{9}{4}+5^{2}\left(\frac{-1}{5}+\frac{2}{5}\right)^{2}+\sqrt{\frac{9}{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{9}{4}+25\left(\frac{-1}{5}+\frac{2}{5}\right)^{2}+\sqrt{\frac{9}{4}}$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$\frac{9}{4}+25\left(-\frac{1}{5}+\frac{2}{5}\right)^{2}+\sqrt{\frac{9}{4}}$$

Add -\frac{1}{5} and \frac{2}{5} to get \frac{1}{5}.

$$\frac{9}{4}+25\times \left(\frac{1}{5}\right)^{2}+\sqrt{\frac{9}{4}}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{9}{4}+25\times \frac{1}{25}+\sqrt{\frac{9}{4}}$$

Multiply 25 and \frac{1}{25} to get 1.

$$\frac{9}{4}+1+\sqrt{\frac{9}{4}}$$

Add \frac{9}{4} and 1 to get \frac{13}{4}.

$$\frac{13}{4}+\sqrt{\frac{9}{4}}$$

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

$$\frac{13}{4}+\frac{3}{2}$$

Add \frac{13}{4} and \frac{3}{2} to get \frac{19}{4}.

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