Solve (5-2sqrt{2})(2+5sqrt{10})

$$( 5 - 2 \sqrt { 2 } ) ( 2 + 5 \sqrt { 10 } )$$

Evaluate

$$25\sqrt{10}+10-4\sqrt{2}-20\sqrt{5}\approx 38.678727705$$

Solution Steps

Apply the distributive property by multiplying each term of 5-2\sqrt{2} by each term of 2+5\sqrt{10}.

$$10+25\sqrt{10}-4\sqrt{2}-10\sqrt{10}\sqrt{2}$$

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}.

$$10+25\sqrt{10}-4\sqrt{2}-10\sqrt{2}\sqrt{5}\sqrt{2}$$

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

$$10+25\sqrt{10}-4\sqrt{2}-10\times 2\sqrt{5}$$

Multiply -10 and 2 to get -20.

$$10+25\sqrt{10}-4\sqrt{2}-20\sqrt{5}$$