Solve (2-5sqrt{5})(3+sqrt{10})

$$( 2 - 5 \sqrt { 5 } ) ( 3 + \sqrt { 10 } )$$

Evaluate

$$2\sqrt{10}+6-15\sqrt{5}-25\sqrt{2}\approx -56.571803401$$

Solution Steps

Apply the distributive property by multiplying each term of 2-5\sqrt{5} by each term of 3+\sqrt{10}.

$$6+2\sqrt{10}-15\sqrt{5}-5\sqrt{5}\sqrt{10}$$

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

$$6+2\sqrt{10}-15\sqrt{5}-5\sqrt{5}\sqrt{5}\sqrt{2}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$6+2\sqrt{10}-15\sqrt{5}-5\times 5\sqrt{2}$$

Multiply -5 and 5 to get -25.

$$6+2\sqrt{10}-15\sqrt{5}-25\sqrt{2}$$