Solve sqrt{48}-2sqrt{32}+sqrt{75}

$$\sqrt { 48 } - 2 \sqrt { 32 } + \sqrt { 75 }$$

Evaluate

$$9\sqrt{3}-8\sqrt{2}\approx 4.274748769$$

Solution Steps

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}.

$$4\sqrt{3}-2\sqrt{32}+\sqrt{75}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Multiply -2 and 4 to get -8.

$$4\sqrt{3}-8\sqrt{2}+\sqrt{75}$$

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}.

$$4\sqrt{3}-8\sqrt{2}+5\sqrt{3}$$

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

$$9\sqrt{3}-8\sqrt{2}$$