Solve (sqrt{8}+sqrt{12})*sqrt{12}

$$( \sqrt { 8 } + \sqrt { 12 } ) \times \sqrt { 12 }$$

Evaluate

$$4\left(\sqrt{6}+3\right)\approx 21.797958971$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\left(2\sqrt{2}+\sqrt{12}\right)\sqrt{12}$$

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}.

$$\left(2\sqrt{2}+2\sqrt{3}\right)\sqrt{12}$$

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}.

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

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

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

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

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

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

$$4\sqrt{6}+4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$4\sqrt{6}+12$$