Solve 8sqrt{3}-5sqrt{12}+4sqrt{7}s

$$8 \sqrt { 3 } - 5 \sqrt { 12 } + 4 \sqrt { 7 } s$$

Evaluate

$$4\sqrt{7}s-2\sqrt{3}$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$8\sqrt{3}-5\times 2\sqrt{3}+4\sqrt{7}s$$

Multiply -5 and 2 to get -10.

$$8\sqrt{3}-10\sqrt{3}+4\sqrt{7}s$$

Combine 8\sqrt{3} and -10\sqrt{3} to get -2\sqrt{3}.

$$-2\sqrt{3}+4\sqrt{7}s$$

Differentiate w.r.t. s

$$4 \sqrt{7} = 10.583005244$$