Solve 3sqrt{6}(sqrt{7}+sqrt{2})

$$3 \sqrt { 6 } ( \sqrt { 7 } + \sqrt { 2 } )$$

Evaluate

$$3\left(\sqrt{42}+2\sqrt{3}\right)\approx 29.834526941$$

Solution Steps

Use the distributive property to multiply 3\sqrt{6} by \sqrt{7}+\sqrt{2}.

$$3\sqrt{6}\sqrt{7}+3\sqrt{6}\sqrt{2}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$3\sqrt{42}+3\sqrt{6}\sqrt{2}$$

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}.

$$3\sqrt{42}+3\sqrt{2}\sqrt{3}\sqrt{2}$$

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

$$3\sqrt{42}+3\times 2\sqrt{3}$$

Multiply 3 and 2 to get 6.

$$3\sqrt{42}+6\sqrt{3}$$