Solve 10sqrt{7}-sqrt{28}+6sqrt{180}

$$10 \sqrt { 7 } - \sqrt { 28 } + 6 \sqrt { 180 }$$

Evaluate

$$8\sqrt{7}+36\sqrt{5}\approx 101.664457679$$

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}.

$$10\sqrt{7}-2\sqrt{7}+6\sqrt{180}$$

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

$$8\sqrt{7}+6\sqrt{180}$$

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$8\sqrt{7}+6\times 6\sqrt{5}$$

Multiply 6 and 6 to get 36.

$$8\sqrt{7}+36\sqrt{5}$$