Solve sqrt{12}left(sqrt{50}-sqrt{18}right)

$$\sqrt{ 12 } \left( \sqrt{ 50 } - \sqrt{ 18 } \right)$$

Evaluate

$$4\sqrt{6}\approx 9.797958971$$

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}.

$$2\sqrt{3}\left(\sqrt{50}-\sqrt{18}\right)$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$2\sqrt{3}\left(5\sqrt{2}-\sqrt{18}\right)$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\sqrt{3}\left(5\sqrt{2}-3\sqrt{2}\right)$$

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

$$2\sqrt{3}\times 2\sqrt{2}$$

Multiply 2 and 2 to get 4.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$4\sqrt{6}$$