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

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

Evaluate

$$3\sqrt{6}+10\sqrt{2}+10\sqrt{3}+6\approx 44.811112928$$

Solution Steps

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

$$3\sqrt{6}+5\sqrt{6}\sqrt{2}+6+10\sqrt{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$3\sqrt{6}+5\sqrt{2}\sqrt{3}\sqrt{2}+6+10\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$3\sqrt{6}+5\times 2\sqrt{3}+6+10\sqrt{2}$$

Multiply 5 and 2 to get 10.

$$3\sqrt{6}+10\sqrt{3}+6+10\sqrt{2}$$