Solve sqrt{75}+sqrt{48}-sqrt{27}

$$\sqrt{ 75 } + \sqrt{ 48 } - \sqrt{ 27 }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

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

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}.

$$5\sqrt{3}+4\sqrt{3}-\sqrt{27}$$

Combine 5\sqrt{3} and 4\sqrt{3} to get 9\sqrt{3}.

$$9\sqrt{3}-\sqrt{27}$$

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}.

$$9\sqrt{3}-3\sqrt{3}$$

Combine 9\sqrt{3} and -3\sqrt{3} to get 6\sqrt{3}.

$$6\sqrt{3}$$