Solve frac{sqrt{3}*(sqrt{15^4}-sqrt{6})}{sqrt{2}}=

$$\frac { \sqrt { 3 } \cdot ( \sqrt { 15 ^ { 4 } } - \sqrt { 6 } ) } { \sqrt { 2 } } =$$

Evaluate

$$\frac{225\sqrt{6}}{2}-3\approx 272.567596063$$

Solution Steps

Calculate 15 to the power of 4 and get 50625.

$$\frac{\sqrt{3}\left(\sqrt{50625}-\sqrt{6}\right)}{\sqrt{2}}$$

Calculate the square root of 50625 and get 225.

$$\frac{\sqrt{3}\left(225-\sqrt{6}\right)}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}\left(225-\sqrt{6}\right)}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\left(225-\sqrt{6}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\left(225-\sqrt{6}\right)\sqrt{2}}{2}$$

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

$$\frac{\sqrt{6}\left(225-\sqrt{6}\right)}{2}$$

Use the distributive property to multiply \sqrt{6} by 225-\sqrt{6}.

$$\frac{225\sqrt{6}-\left(\sqrt{6}\right)^{2}}{2}$$

The square of \sqrt{6} is 6.

$$\frac{225\sqrt{6}-6}{2}$$