Solve V(12sqrt{2})^2+(frac{9sqrt{6}}{2})^2

$$V ( 12 \sqrt { 2 } ) ^ { 2 } + ( \frac { 9 \sqrt { 6 } } { 2 } ) ^ { 2 }$$

Evaluate

$$288V+\frac{243}{2}$$

Solution Steps

Expand \left(12\sqrt{2}\right)^{2}.

$$V\times 12^{2}\left(\sqrt{2}\right)^{2}+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

Calculate 12 to the power of 2 and get 144.

$$V\times 144\left(\sqrt{2}\right)^{2}+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$V\times 144\times 2+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

Multiply 144 and 2 to get 288.

$$V\times 288+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

To raise \frac{9\sqrt{6}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$V\times 288+\frac{\left(9\sqrt{6}\right)^{2}}{2^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply V\times 288 times \frac{2^{2}}{2^{2}}.

$$\frac{V\times 288\times 2^{2}}{2^{2}}+\frac{\left(9\sqrt{6}\right)^{2}}{2^{2}}$$

Since \frac{V\times 288\times 2^{2}}{2^{2}} and \frac{\left(9\sqrt{6}\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$\frac{V\times 288\times 2^{2}+\left(9\sqrt{6}\right)^{2}}{2^{2}}$$

Expand \left(9\sqrt{6}\right)^{2}.

$$V\times 288+\frac{9^{2}\left(\sqrt{6}\right)^{2}}{2^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$V\times 288+\frac{81\left(\sqrt{6}\right)^{2}}{2^{2}}$$

The square of \sqrt{6} is 6.

$$V\times 288+\frac{81\times 6}{2^{2}}$$

Multiply 81 and 6 to get 486.

$$V\times 288+\frac{486}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$V\times 288+\frac{486}{4}$$

Reduce the fraction \frac{486}{4} to lowest terms by extracting and canceling out 2.

$$V\times 288+\frac{243}{2}$$

Expand

$$288V+\frac{243}{2}$$

Solution Steps

Expand \left(12\sqrt{2}\right)^{2}.

$$V\times 12^{2}\left(\sqrt{2}\right)^{2}+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

Calculate 12 to the power of 2 and get 144.

$$V\times 144\left(\sqrt{2}\right)^{2}+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$V\times 144\times 2+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

Multiply 144 and 2 to get 288.

$$V\times 288+\left(\frac{9\sqrt{6}}{2}\right)^{2}$$

To raise \frac{9\sqrt{6}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$V\times 288+\frac{\left(9\sqrt{6}\right)^{2}}{2^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply V\times 288 times \frac{2^{2}}{2^{2}}.

$$\frac{V\times 288\times 2^{2}}{2^{2}}+\frac{\left(9\sqrt{6}\right)^{2}}{2^{2}}$$

Since \frac{V\times 288\times 2^{2}}{2^{2}} and \frac{\left(9\sqrt{6}\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$\frac{V\times 288\times 2^{2}+\left(9\sqrt{6}\right)^{2}}{2^{2}}$$

Expand \left(9\sqrt{6}\right)^{2}.

$$V\times 288+\frac{9^{2}\left(\sqrt{6}\right)^{2}}{2^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$V\times 288+\frac{81\left(\sqrt{6}\right)^{2}}{2^{2}}$$

The square of \sqrt{6} is 6.

$$V\times 288+\frac{81\times 6}{2^{2}}$$

Multiply 81 and 6 to get 486.

$$V\times 288+\frac{486}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$V\times 288+\frac{486}{4}$$

Reduce the fraction \frac{486}{4} to lowest terms by extracting and canceling out 2.

$$V\times 288+\frac{243}{2}$$