Solve sqrt{75}+sqrt{48}+(-7sqrt{3})

$$\sqrt { 75 } + \sqrt { 48 } + ( - 7 \sqrt { 3 } )$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

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}.

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

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}.

$$5\sqrt{3}+4\sqrt{3}-7\sqrt{3}$$

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

$$9\sqrt{3}-7\sqrt{3}$$

Combine 9\sqrt{3} and -7\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$