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

$$\sqrt { 1 + ( 2 / 3 ) ^ { 2 } - 4 / 3 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

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

$$\sqrt{1+\frac{4}{9}-\frac{4}{3}}$$

Convert 1 to fraction \frac{9}{9}.

$$\sqrt{\frac{9}{9}+\frac{4}{9}-\frac{4}{3}}$$

Since \frac{9}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{9+4}{9}-\frac{4}{3}}$$

Add 9 and 4 to get 13.

$$\sqrt{\frac{13}{9}-\frac{4}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{13}{9} and \frac{4}{3} to fractions with denominator 9.

$$\sqrt{\frac{13}{9}-\frac{12}{9}}$$

Since \frac{13}{9} and \frac{12}{9} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{13-12}{9}}$$

Subtract 12 from 13 to get 1.

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

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$