Solve 5sqrt{27}-2sqrt{48}

$$5 \sqrt { 27 } - 2 \sqrt { 48 }$$

Evaluate

$$7\sqrt{3}\approx 12.124355653$$

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}.

$$5\times 3\sqrt{3}-2\sqrt{48}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{3}-2\sqrt{48}$$

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}.

$$15\sqrt{3}-2\times 4\sqrt{3}$$

Multiply -2 and 4 to get -8.

$$15\sqrt{3}-8\sqrt{3}$$

Combine 15\sqrt{3} and -8\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}$$