Solve 2sqrt{5}sqrt{15}+sqrt{12}

$$2 \sqrt{ 5 } \sqrt{ 15 } + \sqrt{ 12 }$$

Evaluate

$$12\sqrt{3}\approx 20.784609691$$

Solution Steps

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

$$2\sqrt{5}\sqrt{5}\sqrt{3}+\sqrt{12}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$2\times 5\sqrt{3}+\sqrt{12}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}+\sqrt{12}$$

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}.

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

Combine 10\sqrt{3} and 2\sqrt{3} to get 12\sqrt{3}.

$$12\sqrt{3}$$