Solve 2sqrt{7}+4sqrt{28}-5sqrt{175}

$$2 \sqrt{ 7 } +4 \sqrt{ 28 } -5 \sqrt{ 175 }$$

Evaluate

$$-15\sqrt{7}\approx -39.686269666$$

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}.

$$2\sqrt{7}+4\times 2\sqrt{7}-5\sqrt{175}$$

Multiply 4 and 2 to get 8.

$$2\sqrt{7}+8\sqrt{7}-5\sqrt{175}$$

Combine 2\sqrt{7} and 8\sqrt{7} to get 10\sqrt{7}.

$$10\sqrt{7}-5\sqrt{175}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$10\sqrt{7}-5\times 5\sqrt{7}$$

Multiply -5 and 5 to get -25.

$$10\sqrt{7}-25\sqrt{7}$$

Combine 10\sqrt{7} and -25\sqrt{7} to get -15\sqrt{7}.

$$-15\sqrt{7}$$