Solve (3+sqrt{2})^2-4(2-sqrt{2})

$$( 3 + \sqrt { 2 } ) ^ { 2 } - 4 ( 2 - \sqrt { 2 } )$$

Evaluate

$$10\sqrt{2}+3\approx 17.142135624$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+\sqrt{2}\right)^{2}.

$$9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}-4\left(2-\sqrt{2}\right)$$

The square of \sqrt{2} is 2.

$$9+6\sqrt{2}+2-4\left(2-\sqrt{2}\right)$$

Add 9 and 2 to get 11.

$$11+6\sqrt{2}-4\left(2-\sqrt{2}\right)$$

Use the distributive property to multiply -4 by 2-\sqrt{2}.

$$11+6\sqrt{2}-8+4\sqrt{2}$$

Subtract 8 from 11 to get 3.

$$3+6\sqrt{2}+4\sqrt{2}$$

Combine 6\sqrt{2} and 4\sqrt{2} to get 10\sqrt{2}.

$$3+10\sqrt{2}$$