Solve sqrt{28}+4sqrt{80}-3sqrt{70}

$$\sqrt { 28 } + 4 \sqrt { 80 } - 3 \sqrt { 70 }$$

Evaluate

$$2\sqrt{7}+16\sqrt{5}-3\sqrt{70}\approx 15.968789466$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$2\sqrt{7}+4\sqrt{80}-3\sqrt{70}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$2\sqrt{7}+4\times 4\sqrt{5}-3\sqrt{70}$$

Multiply 4 and 4 to get 16.

$$2\sqrt{7}+16\sqrt{5}-3\sqrt{70}$$