Solve (sqrt{24}+sqrt{25})-(sqrt{8}-sqrt{6})

$$( \sqrt { 24 } + \sqrt { 25 } ) - ( \sqrt { 8 } - \sqrt { 6 } )$$

Evaluate

$$3\sqrt{6}+5-2\sqrt{2}\approx 9.520042104$$

Solution Steps

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}.

$$2\sqrt{6}+\sqrt{25}-\left(\sqrt{8}-\sqrt{6}\right)$$

Calculate the square root of 25 and get 5.

$$2\sqrt{6}+5-\left(\sqrt{8}-\sqrt{6}\right)$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

To find the opposite of 2\sqrt{2}-\sqrt{6}, find the opposite of each term.

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

The opposite of -\sqrt{6} is \sqrt{6}.

$$2\sqrt{6}+5-2\sqrt{2}+\sqrt{6}$$

Combine 2\sqrt{6} and \sqrt{6} to get 3\sqrt{6}.

$$3\sqrt{6}+5-2\sqrt{2}$$