Solve (sqrt{12}+sqrt{15})*sqrt{3}

$$( \sqrt { 12 } + \sqrt { 15 } ) \cdot \sqrt { 3 }$$

Evaluate

$$3\left(\sqrt{5}+2\right)\approx 12.708203932$$

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}.

$$\left(2\sqrt{3}+\sqrt{15}\right)\sqrt{3}$$

Use the distributive property to multiply 2\sqrt{3}+\sqrt{15} by \sqrt{3}.

$$2\left(\sqrt{3}\right)^{2}+\sqrt{15}\sqrt{3}$$

The square of \sqrt{3} is 3.

$$2\times 3+\sqrt{15}\sqrt{3}$$

Multiply 2 and 3 to get 6.

$$6+\sqrt{15}\sqrt{3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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