Solve 1-(frac{14sqrt{3}}{3})^2=(7)^2

$$1 - ( \frac { 14 \sqrt { 3 } } { 3 } ) ^ { 2 } = ( 7 ) ^ { 2 }$$

Verify

Solution Steps

To raise \frac{14\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$1-\frac{\left(14\sqrt{3}\right)^{2}}{3^{2}}=7^{2}$$

Expand \left(14\sqrt{3}\right)^{2}.

$$1-\frac{14^{2}\left(\sqrt{3}\right)^{2}}{3^{2}}=7^{2}$$

Calculate 14 to the power of 2 and get 196.

$$1-\frac{196\left(\sqrt{3}\right)^{2}}{3^{2}}=7^{2}$$

The square of \sqrt{3} is 3.

$$1-\frac{196\times 3}{3^{2}}=7^{2}$$

Multiply 196 and 3 to get 588.

$$1-\frac{588}{3^{2}}=7^{2}$$

Calculate 3 to the power of 2 and get 9.

$$1-\frac{588}{9}=7^{2}$$

Reduce the fraction \frac{588}{9} to lowest terms by extracting and canceling out 3.

$$1-\frac{196}{3}=7^{2}$$

Subtract \frac{196}{3} from 1 to get -\frac{193}{3}.

$$-\frac{193}{3}=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$-\frac{193}{3}=49$$

Convert 49 to fraction \frac{147}{3}.

$$-\frac{193}{3}=\frac{147}{3}$$

Compare -\frac{193}{3} and \frac{147}{3}.

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