Solve [7]2sqrt{11}+3sqrt{44}+sqrt{123}

$$[ 7 ] 2 \sqrt { 11 } + 3 \sqrt { 44 } + \sqrt { 123 }$$

Evaluate

$$\sqrt{123}+20\sqrt{11}\approx 77.423032314$$

Solution Steps

Multiply 2 and 7 to get 14.

$$14\sqrt{11}+3\sqrt{44}+\sqrt{123}$$

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

$$14\sqrt{11}+3\times 2\sqrt{11}+\sqrt{123}$$

Multiply 3 and 2 to get 6.

$$14\sqrt{11}+6\sqrt{11}+\sqrt{123}$$

Combine 14\sqrt{11} and 6\sqrt{11} to get 20\sqrt{11}.

$$20\sqrt{11}+\sqrt{123}$$