Solve (1)(sqrt{12}+5sqrt{8})*sqrt{3}

$$( 1 ) ( \sqrt { 12 } + 5 \sqrt { 8 } ) \times \sqrt { 3 }$$

Evaluate

$$10\sqrt{6}+6\approx 30.494897428$$

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}.

$$1\left(2\sqrt{3}+5\sqrt{8}\right)\sqrt{3}$$

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}.

$$1\left(2\sqrt{3}+5\times 2\sqrt{2}\right)\sqrt{3}$$

Multiply 5 and 2 to get 10.

$$1\left(2\sqrt{3}+10\sqrt{2}\right)\sqrt{3}$$

Use the distributive property to multiply 1 by 2\sqrt{3}+10\sqrt{2}.

$$\left(2\sqrt{3}+10\sqrt{2}\right)\sqrt{3}$$

Use the distributive property to multiply 2\sqrt{3}+10\sqrt{2} by \sqrt{3}.

$$2\left(\sqrt{3}\right)^{2}+10\sqrt{2}\sqrt{3}$$

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

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

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