Solve (2sqrt{2}+3)(17-12sqrt{2})

$$(2 \sqrt{ 2 } +3)(17-12 \sqrt{ 2 } )$$

Evaluate

$$3-2\sqrt{2}\approx 0.171572875$$

Solution Steps

Apply the distributive property by multiplying each term of 2\sqrt{2}+3 by each term of 17-12\sqrt{2}.

$$34\sqrt{2}-24\left(\sqrt{2}\right)^{2}+51-36\sqrt{2}$$

The square of \sqrt{2} is 2.

$$34\sqrt{2}-24\times 2+51-36\sqrt{2}$$

Multiply -24 and 2 to get -48.

$$34\sqrt{2}-48+51-36\sqrt{2}$$

Add -48 and 51 to get 3.

$$34\sqrt{2}+3-36\sqrt{2}$$

Combine 34\sqrt{2} and -36\sqrt{2} to get -2\sqrt{2}.

$$-2\sqrt{2}+3$$