Solve (sqrt{6}+sqrt{3})sqrt{6}-sqrt{3})

$$( \sqrt { 6 } + \sqrt { 3 } ) \sqrt { 6 } - \sqrt { 3 } )$$

Evaluate

$$3\sqrt{2}+6-\sqrt{3}\approx 8.51058988$$

Solution Steps

Use the distributive property to multiply \sqrt{6}+\sqrt{3} by \sqrt{6}.

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

The square of \sqrt{6} is 6.

$$6+\sqrt{3}\sqrt{6}-\sqrt{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$6+\sqrt{3}\sqrt{3}\sqrt{2}-\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$6+3\sqrt{2}-\sqrt{3}$$