Solve sqrt{27}+sqrt{48}+sqrt{75}div3

$$\sqrt { 27 } + \sqrt { 48 } + \sqrt { 75 } \div 3$$

Evaluate

$$\frac{26\sqrt{3}}{3}\approx 15.011106999$$

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}.

$$3\sqrt{3}+\sqrt{48}+\frac{\sqrt{75}}{3}$$

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}.

$$3\sqrt{3}+4\sqrt{3}+\frac{\sqrt{75}}{3}$$

Combine 3\sqrt{3} and 4\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}+\frac{\sqrt{75}}{3}$$

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}.

$$7\sqrt{3}+\frac{5\sqrt{3}}{3}$$

Combine 7\sqrt{3} and \frac{5\sqrt{3}}{3} to get \frac{26}{3}\sqrt{3}.

$$\frac{26}{3}\sqrt{3}$$