Solve sqrt{(sqrt{30})^2-(sqrt{6})^2}

$$\sqrt { ( \sqrt { 30 } ) ^ { 2 } - ( \sqrt { 6 } ) ^ { 2 } }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

The square of \sqrt{30} is 30.

$$\sqrt{30-\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\sqrt{30-6}$$

Subtract 6 from 30 to get 24.

$$\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$2\sqrt{6}$$