Solve c=sqrt{588}-sqrt{300}+sqrt{100}-21sqrt{3-1}

$$c = \sqrt { 588 } - \sqrt { 300 } + \sqrt { 100 } - 21 \sqrt { 3 - 1 }$$

Solve for c

$$c=4\sqrt{3}+10-21\sqrt{2}\approx -12.77028158$$

Steps for Solving Linear Equation

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}.

$$c=14\sqrt{3}-\sqrt{300}+\sqrt{100}-21\sqrt{3-1}$$

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}.

$$c=14\sqrt{3}-10\sqrt{3}+\sqrt{100}-21\sqrt{3-1}$$

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

$$c=4\sqrt{3}+\sqrt{100}-21\sqrt{3-1}$$

Calculate the square root of 100 and get 10.

$$c=4\sqrt{3}+10-21\sqrt{3-1}$$

Subtract 1 from 3 to get 2.

$$c=4\sqrt{3}+10-21\sqrt{2}$$

Assign c

$$c≔4\sqrt{3}+10-21\sqrt{2}$$