Solve (sqrt{12}+sqrt{32})sqrt{3}=

$$( \sqrt { 12 } + \sqrt { 32 } ) \sqrt { 3 } =$$

Evaluate

$$4\sqrt{6}+6\approx 15.797958971$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\left(2\sqrt{3}+\sqrt{32}\right)\sqrt{3}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\left(2\sqrt{3}+4\sqrt{2}\right)\sqrt{3}$$

Use the distributive property to multiply 2\sqrt{3}+4\sqrt{2} by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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