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

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

Evaluate

$$2\left(\sqrt{15}+3\right)\approx 13.745966692$$

Solution Steps

Factor 12=1\times 12. Rewrite the square root of the product \sqrt{1\times 12} as the product of square roots \sqrt{1}\sqrt{12}.

$$\left(\sqrt{5}+\sqrt{3}\right)\sqrt{1}\sqrt{1}\sqrt{12}$$

Multiply \sqrt{1} and \sqrt{1} to get 1.

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

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}.

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

Multiply 1 and 2 to get 2.

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

Use the distributive property to multiply \sqrt{5}+\sqrt{3} by 2.

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

Use the distributive property to multiply 2\sqrt{5}+2\sqrt{3} by \sqrt{3}.

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

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

$$2\sqrt{15}+6$$