Solve (sqrt{20}-3)(sqrt{5}+8)

$$( \sqrt { 20 } - 3 ) ( \sqrt { 5 } + 8 )$$

Evaluate

$$13\sqrt{5}-14\approx 15.068883707$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\left(2\sqrt{5}-3\right)\left(\sqrt{5}+8\right)$$

Apply the distributive property by multiplying each term of 2\sqrt{5}-3 by each term of \sqrt{5}+8.

$$2\left(\sqrt{5}\right)^{2}+16\sqrt{5}-3\sqrt{5}-24$$

The square of \sqrt{5} is 5.

$$2\times 5+16\sqrt{5}-3\sqrt{5}-24$$

Multiply 2 and 5 to get 10.

$$10+16\sqrt{5}-3\sqrt{5}-24$$

Combine 16\sqrt{5} and -3\sqrt{5} to get 13\sqrt{5}.

$$10+13\sqrt{5}-24$$

Subtract 24 from 10 to get -14.

$$-14+13\sqrt{5}$$