Solve 2sqrt{3}-5sqrt{27}+7sqrt{48}

$$2 \sqrt { 3 } - 5 \sqrt { 27 } + 7 \sqrt { 48 }$$

Evaluate

$$15\sqrt{3}\approx 25.980762114$$

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}.

$$2\sqrt{3}-5\times 3\sqrt{3}+7\sqrt{48}$$

Multiply -5 and 3 to get -15.

$$2\sqrt{3}-15\sqrt{3}+7\sqrt{48}$$

Combine 2\sqrt{3} and -15\sqrt{3} to get -13\sqrt{3}.

$$-13\sqrt{3}+7\sqrt{48}$$

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}.

$$-13\sqrt{3}+7\times 4\sqrt{3}$$

Multiply 7 and 4 to get 28.

$$-13\sqrt{3}+28\sqrt{3}$$

Combine -13\sqrt{3} and 28\sqrt{3} to get 15\sqrt{3}.

$$15\sqrt{3}$$