Solve (3sqrt{2}+5)(6sqrt{2}-1)

$$(3 \sqrt{ 2 } +5)(6 \sqrt{ 2 } -1)$$

Evaluate

$$27\sqrt{2}+31\approx 69.183766184$$

Solution Steps

Apply the distributive property by multiplying each term of 3\sqrt{2}+5 by each term of 6\sqrt{2}-1.

$$18\left(\sqrt{2}\right)^{2}-3\sqrt{2}+30\sqrt{2}-5$$

The square of \sqrt{2} is 2.

$$18\times 2-3\sqrt{2}+30\sqrt{2}-5$$

Multiply 18 and 2 to get 36.

$$36-3\sqrt{2}+30\sqrt{2}-5$$

Combine -3\sqrt{2} and 30\sqrt{2} to get 27\sqrt{2}.

$$36+27\sqrt{2}-5$$

Subtract 5 from 36 to get 31.

$$31+27\sqrt{2}$$