Solve sqrt{3}+sqrt{8}ksqrt{11}

$$\sqrt { 3 } + \sqrt { 8 } k \sqrt { 11 }$$

Evaluate

$$2\sqrt{22}k+\sqrt{3}$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\sqrt{3}+2\sqrt{2}k\sqrt{11}$$

To multiply \sqrt{2} and \sqrt{11}, multiply the numbers under the square root.

$$\sqrt{3}+2\sqrt{22}k$$

Differentiate w.r.t. k

$$2 \sqrt{22} = 9.38083152$$