Solve sqrt{23*2/3-14-3*(2/3)^2}=0

$$\sqrt { 23 \cdot \frac { 2 } { 3 } - 14 - 3 \cdot ( \frac { 2 } { 3 } ) ^ { 2 } } = 0$$

Verify

Solution Steps

Express 23\times \frac{2}{3} as a single fraction.

$$\sqrt{\frac{23\times 2}{3}-14-3\times \left(\frac{2}{3}\right)^{2}}=0$$

Multiply 23 and 2 to get 46.

$$\sqrt{\frac{46}{3}-14-3\times \left(\frac{2}{3}\right)^{2}}=0$$

Convert 14 to fraction \frac{42}{3}.

$$\sqrt{\frac{46}{3}-\frac{42}{3}-3\times \left(\frac{2}{3}\right)^{2}}=0$$

Since \frac{46}{3} and \frac{42}{3} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{46-42}{3}-3\times \left(\frac{2}{3}\right)^{2}}=0$$

Subtract 42 from 46 to get 4.

$$\sqrt{\frac{4}{3}-3\times \left(\frac{2}{3}\right)^{2}}=0$$

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

$$\sqrt{\frac{4}{3}-3\times \frac{4}{9}}=0$$

Express 3\times \frac{4}{9} as a single fraction.

$$\sqrt{\frac{4}{3}-\frac{3\times 4}{9}}=0$$

Multiply 3 and 4 to get 12.

$$\sqrt{\frac{4}{3}-\frac{12}{9}}=0$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{4}{3}-\frac{4}{3}}=0$$

Subtract \frac{4}{3} from \frac{4}{3} to get 0.

$$\sqrt{0}=0$$

Calculate the square root of 0 and get 0.

$$0=0$$

Compare 0 and 0.

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