Solve (sqrt{2}+4)(4sqrt{10}-2)

$$( \sqrt { 2 } + 4 ) ( 4 \sqrt { 10 } - 2 )$$

Evaluate

$$8\sqrt{5}+16\sqrt{10}-2\sqrt{2}-8\approx 57.656559258$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{2}+4 by each term of 4\sqrt{10}-2.

$$4\sqrt{2}\sqrt{10}-2\sqrt{2}+16\sqrt{10}-8$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$4\sqrt{2}\sqrt{2}\sqrt{5}-2\sqrt{2}+16\sqrt{10}-8$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$4\times 2\sqrt{5}-2\sqrt{2}+16\sqrt{10}-8$$

Multiply 4 and 2 to get 8.

$$8\sqrt{5}-2\sqrt{2}+16\sqrt{10}-8$$

Factor

$$2 {(4 \sqrt{5} + 8 \sqrt{10} - \sqrt{2} - 4)} = 57.656559258$$