Solve sqrt{75}-sqrt{3}-sqrt{32}

$$\sqrt{ 75 } - \sqrt{ 3 } - \sqrt{ 32 }$$

Evaluate

$$4\left(\sqrt{3}-\sqrt{2}\right)\approx 1.271348981$$

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}.

$$5\sqrt{3}-\sqrt{3}-\sqrt{32}$$

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

$$4\sqrt{3}-\sqrt{32}$$

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}.

$$4\sqrt{3}-4\sqrt{2}$$