Solve (2/3)^2+(1/4)^-2-(sqrt{4/9}-1/2)=16.111

$$( \frac { 2 } { 3 } ) ^ { 2 } + ( \frac { 1 } { 4 } ) ^ { - 2 } - ( \sqrt { \frac { 4 } { 9 } } - \frac { 1 } { 2 } ) = 16.111$$

Verify

Solution Steps

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

$$\frac{4}{9}+\left(\frac{1}{4}\right)^{-2}-\left(\sqrt{\frac{4}{9}}-\frac{1}{2}\right)=16.111$$

Calculate \frac{1}{4} to the power of -2 and get 16.

$$\frac{4}{9}+16-\left(\sqrt{\frac{4}{9}}-\frac{1}{2}\right)=16.111$$

Add \frac{4}{9} and 16 to get \frac{148}{9}.

$$\frac{148}{9}-\left(\sqrt{\frac{4}{9}}-\frac{1}{2}\right)=16.111$$

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.

$$\frac{148}{9}-\left(\frac{2}{3}-\frac{1}{2}\right)=16.111$$

Subtract \frac{1}{2} from \frac{2}{3} to get \frac{1}{6}.

$$\frac{148}{9}-\frac{1}{6}=16.111$$

Subtract \frac{1}{6} from \frac{148}{9} to get \frac{293}{18}.

$$\frac{293}{18}=16.111$$

Convert decimal number 16.111 to fraction \frac{16111}{1000}.

$$\frac{293}{18}=\frac{16111}{1000}$$

Least common multiple of 18 and 1000 is 9000. Convert \frac{293}{18} and \frac{16111}{1000} to fractions with denominator 9000.

$$\frac{146500}{9000}=\frac{144999}{9000}$$

Compare \frac{146500}{9000} and \frac{144999}{9000}.

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