Solve 4sqrt{12}-5sqrt{11}+1sqrt{192}

$$4 \sqrt { 12 } - 5 \sqrt { 11 } + 1 \sqrt { 192 }$$

Evaluate

$$16\sqrt{3}-5\sqrt{11}\approx 11.129688969$$

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}.

$$4\times 2\sqrt{3}-5\sqrt{11}+1\sqrt{192}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}-5\sqrt{11}+1\sqrt{192}$$

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

$$8\sqrt{3}-5\sqrt{11}+1\times 8\sqrt{3}$$

Multiply 1 and 8 to get 8.

$$8\sqrt{3}-5\sqrt{11}+8\sqrt{3}$$

Combine 8\sqrt{3} and 8\sqrt{3} to get 16\sqrt{3}.

$$16\sqrt{3}-5\sqrt{11}$$