Solve sqrt{588}-sqrt{300}+sqrt{108}-21sqrt{8-1}

$$\sqrt { 588 } - \sqrt { 300 } + \sqrt { 108 } - 21 \sqrt { 8 - 1 }$$

Evaluate

$$10\sqrt{3}-21\sqrt{7}\approx -38.240269457$$

Solution Steps

Factor 588=14^{2}\times 3. Rewrite the square root of the product \sqrt{14^{2}\times 3} as the product of square roots \sqrt{14^{2}}\sqrt{3}. Take the square root of 14^{2}.

$$14\sqrt{3}-\sqrt{300}+\sqrt{108}-21\sqrt{8-1}$$

Factor 300=10^{2}\times 3. Rewrite the square root of the product \sqrt{10^{2}\times 3} as the product of square roots \sqrt{10^{2}}\sqrt{3}. Take the square root of 10^{2}.

$$14\sqrt{3}-10\sqrt{3}+\sqrt{108}-21\sqrt{8-1}$$

Combine 14\sqrt{3} and -10\sqrt{3} to get 4\sqrt{3}.

$$4\sqrt{3}+\sqrt{108}-21\sqrt{8-1}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$4\sqrt{3}+6\sqrt{3}-21\sqrt{8-1}$$

Combine 4\sqrt{3} and 6\sqrt{3} to get 10\sqrt{3}.

$$10\sqrt{3}-21\sqrt{8-1}$$

Subtract 1 from 8 to get 7.

$$10\sqrt{3}-21\sqrt{7}$$