Solve 5sqrt{3}+2sqrt{12}-sqrt{18}

$$5 \sqrt { 3 } + 2 \sqrt { 12 } - \sqrt { 18 }$$

Evaluate

$$3^{\frac{5}{2}}-3\sqrt{2}\approx 11.345816581$$

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}.

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

Multiply 2 and 2 to get 4.

$$5\sqrt{3}+4\sqrt{3}-\sqrt{18}$$

Combine 5\sqrt{3} and 4\sqrt{3} to get 9\sqrt{3}.

$$9\sqrt{3}-\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$9\sqrt{3}-3\sqrt{2}$$