Solve sqrt{243}-sqrt{75}

$$\sqrt{ 243 } - \sqrt{ 75 }$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Solution Steps

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$9\sqrt{3}-\sqrt{75}$$

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}.

$$9\sqrt{3}-5\sqrt{3}$$

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

$$4\sqrt{3}$$