Solve (5-3sqrt{2})^2+6sqrt{50}

$$( 5 - 3 \sqrt { 2 } ) ^ { 2 } + 6 \sqrt { 50 }$$

Evaluate

$$43$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-3\sqrt{2}\right)^{2}.

$$25-30\sqrt{2}+9\left(\sqrt{2}\right)^{2}+6\sqrt{50}$$

The square of \sqrt{2} is 2.

$$25-30\sqrt{2}+9\times 2+6\sqrt{50}$$

Multiply 9 and 2 to get 18.

$$25-30\sqrt{2}+18+6\sqrt{50}$$

Add 25 and 18 to get 43.

$$43-30\sqrt{2}+6\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$43-30\sqrt{2}+6\times 5\sqrt{2}$$

Multiply 6 and 5 to get 30.

$$43-30\sqrt{2}+30\sqrt{2}$$

Combine -30\sqrt{2} and 30\sqrt{2} to get 0.

$$43$$

Factor

$$43$$