Solve (2sqrt{3/2})^2-sqrt{(-5)^2}

$$( 2 \sqrt { \frac { 3 } { 2 } } ) ^ { 2 } - \sqrt { ( - 5 ) ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\left(2\times \frac{\sqrt{3}}{\sqrt{2}}\right)^{2}-\sqrt{\left(-5\right)^{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\left(2\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}-\sqrt{\left(-5\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\left(2\times \frac{\sqrt{3}\sqrt{2}}{2}\right)^{2}-\sqrt{\left(-5\right)^{2}}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\left(2\times \frac{\sqrt{6}}{2}\right)^{2}-\sqrt{\left(-5\right)^{2}}$$

Cancel out 2 and 2.

$$\left(\sqrt{6}\right)^{2}-\sqrt{\left(-5\right)^{2}}$$

The square of \sqrt{6} is 6.

$$6-\sqrt{\left(-5\right)^{2}}$$

Calculate -5 to the power of 2 and get 25.

$$6-\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$6-5$$

Subtract 5 from 6 to get 1.

$$1$$

Factor

$$1$$