Solve 9sqrt{12}+3sqrt{20}

$$9 \sqrt { 12 } + 3 \sqrt { 20 }$$

Evaluate

$$6\left(\sqrt{5}+3\sqrt{3}\right)\approx 44.593322401$$

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}.

$$9\times 2\sqrt{3}+3\sqrt{20}$$

Multiply 9 and 2 to get 18.

$$18\sqrt{3}+3\sqrt{20}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$18\sqrt{3}+3\times 2\sqrt{5}$$

Multiply 3 and 2 to get 6.

$$18\sqrt{3}+6\sqrt{5}$$

Factor

$$6 {(\sqrt{5} + 3 \sqrt{3})} = 44.593322401$$