Solve 5sqrt{27}+sqrt{12}+5sqrt{48}

$$5 \sqrt{ 27 } + \sqrt{ 12 } +5 \sqrt{ 48 }$$

Evaluate

$$37\sqrt{3}\approx 64.08587988$$

Solution Steps

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}.

$$5\times 3\sqrt{3}+\sqrt{12}+5\sqrt{48}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{3}+\sqrt{12}+5\sqrt{48}$$

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}.

$$15\sqrt{3}+2\sqrt{3}+5\sqrt{48}$$

Combine 15\sqrt{3} and 2\sqrt{3} to get 17\sqrt{3}.

$$17\sqrt{3}+5\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$17\sqrt{3}+5\times 4\sqrt{3}$$

Multiply 5 and 4 to get 20.

$$17\sqrt{3}+20\sqrt{3}$$

Combine 17\sqrt{3} and 20\sqrt{3} to get 37\sqrt{3}.

$$37\sqrt{3}$$