Solve 3sqrt{175}-5sqrt{28}

$$3 \sqrt { 175 } - 5 \sqrt { 28 }$$

Evaluate

$$5\sqrt{7}\approx 13.228756555$$

Solution Steps

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}.

$$3\times 5\sqrt{7}-5\sqrt{28}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{7}-5\sqrt{28}$$

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}.

$$15\sqrt{7}-5\times 2\sqrt{7}$$

Multiply -5 and 2 to get -10.

$$15\sqrt{7}-10\sqrt{7}$$

Combine 15\sqrt{7} and -10\sqrt{7} to get 5\sqrt{7}.

$$5\sqrt{7}$$