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

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

Evaluate

$$46\sqrt{2}\approx 65.053823869$$

Solution Steps

Use the distributive property to multiply 2 by 5-\sqrt{2}.

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

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

$$50\sqrt{2}+20-10\left(\sqrt{2}\right)^{2}-4\sqrt{2}$$

The square of \sqrt{2} is 2.

$$50\sqrt{2}+20-10\times 2-4\sqrt{2}$$

Multiply -10 and 2 to get -20.

$$50\sqrt{2}+20-20-4\sqrt{2}$$

Subtract 20 from 20 to get 0.

$$50\sqrt{2}-4\sqrt{2}$$

Combine 50\sqrt{2} and -4\sqrt{2} to get 46\sqrt{2}.

$$46\sqrt{2}$$