Solve sqrt{75}-2sqrt{2}*sqrt{24}

$$\sqrt { 75 } - 2 \sqrt { 2 } \times \sqrt { 24 }$$

Evaluate

$$-3\sqrt{3}\approx -5.196152423$$

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}.

$$5\sqrt{3}-2\sqrt{2}\sqrt{24}$$

Factor 24=2\times 12. Rewrite the square root of the product \sqrt{2\times 12} as the product of square roots \sqrt{2}\sqrt{12}.

$$5\sqrt{3}-2\sqrt{2}\sqrt{2}\sqrt{12}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$5\sqrt{3}-2\times 2\sqrt{12}$$

Multiply 2 and 2 to get 4.

$$5\sqrt{3}-4\sqrt{12}$$

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}.

$$5\sqrt{3}-4\times 2\sqrt{3}$$

Multiply 4 and 2 to get 8.

$$5\sqrt{3}-8\sqrt{3}$$

Combine 5\sqrt{3} and -8\sqrt{3} to get -3\sqrt{3}.

$$-3\sqrt{3}$$