Solve sqrt{12}-sqrt{45}-sqrt{48}+sqrt{75}

$$\sqrt { 12 } - \sqrt { 45 } - \sqrt { 48 } + \sqrt { 75 }$$

Evaluate

$$3\sqrt{3}-3\sqrt{5}\approx -1.51205151$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{3}-\sqrt{45}-\sqrt{48}+\sqrt{75}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$2\sqrt{3}-3\sqrt{5}-\sqrt{48}+\sqrt{75}$$

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}.

$$2\sqrt{3}-3\sqrt{5}-4\sqrt{3}+\sqrt{75}$$

Combine 2\sqrt{3} and -4\sqrt{3} to get -2\sqrt{3}.

$$-2\sqrt{3}-3\sqrt{5}+\sqrt{75}$$

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}.

$$-2\sqrt{3}-3\sqrt{5}+5\sqrt{3}$$

Combine -2\sqrt{3} and 5\sqrt{3} to get 3\sqrt{3}.

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