Solve (sqrt{3}+5)*(sqrt{8}-3

$$( \sqrt { 3 } + 5 ) \times ( \sqrt { 8 } - 3$$

Evaluate

$$2\sqrt{6}+10\sqrt{2}-3\sqrt{3}-15\approx -1.155037313$$

Solution Steps

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}.

$$\left(\sqrt{3}+5\right)\left(2\sqrt{2}-3\right)$$

Apply the distributive property by multiplying each term of \sqrt{3}+5 by each term of 2\sqrt{2}-3.

$$2\sqrt{3}\sqrt{2}-3\sqrt{3}+10\sqrt{2}-15$$

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

$$2\sqrt{6}-3\sqrt{3}+10\sqrt{2}-15$$