Solve sqrt{25}+sqrt{27}-sqrt{48}=

$$\sqrt { 25 } + \sqrt { 27 } - \sqrt { 48 } =$$

Evaluate

$$5-\sqrt{3}\approx 3.267949192$$

Solution Steps

Calculate the square root of 25 and get 5.

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

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}.

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

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}.

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

Combine 3\sqrt{3} and -4\sqrt{3} to get -\sqrt{3}.

$$5-\sqrt{3}$$