Solve 2sqrt{40}+2sqrt{12}

$$2 \sqrt{ 40 } +2 \sqrt{ 12 }$$

Evaluate

$$4\left(\sqrt{3}+\sqrt{10}\right)\approx 19.577313871$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$2\times 2\sqrt{10}+2\sqrt{12}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{10}+2\sqrt{12}$$

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}.

$$4\sqrt{10}+2\times 2\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{10}+4\sqrt{3}$$

Factor

$$4 {(\sqrt{3} + \sqrt{10})} = 19.577313871$$