Solve 2sqrt{3}+5sqrt{12}-sqrt{27}+sqrt[3]{243}

$$2 \sqrt { 3 } + 5 \sqrt { 12 } - \sqrt { 27 } + \sqrt[ 3 ] { 243 }$$

Evaluate

$$3^{\frac{5}{3}}+3^{\frac{5}{2}}\approx 21.828708737$$

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}.

$$2\sqrt{3}+5\times 2\sqrt{3}-\sqrt{27}+\sqrt[3]{243}$$

Multiply 5 and 2 to get 10.

$$2\sqrt{3}+10\sqrt{3}-\sqrt{27}+\sqrt[3]{243}$$

Combine 2\sqrt{3} and 10\sqrt{3} to get 12\sqrt{3}.

$$12\sqrt{3}-\sqrt{27}+\sqrt[3]{243}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$12\sqrt{3}-3\sqrt{3}+\sqrt[3]{243}$$

Combine 12\sqrt{3} and -3\sqrt{3} to get 9\sqrt{3}.

$$9\sqrt{3}+\sqrt[3]{243}$$