Solve 3sqrt{288}-9sqrt{72}

$$3 \sqrt { 288 } - 9 \sqrt { 72 }$$

Evaluate

$$-18\sqrt{2}\approx -25.455844123$$

Solution Steps

Factor 288=12^{2}\times 2. Rewrite the square root of the product \sqrt{12^{2}\times 2} as the product of square roots \sqrt{12^{2}}\sqrt{2}. Take the square root of 12^{2}.

$$3\times 12\sqrt{2}-9\sqrt{72}$$

Multiply 3 and 12 to get 36.

$$36\sqrt{2}-9\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$36\sqrt{2}-9\times 6\sqrt{2}$$

Multiply -9 and 6 to get -54.

$$36\sqrt{2}-54\sqrt{2}$$

Combine 36\sqrt{2} and -54\sqrt{2} to get -18\sqrt{2}.

$$-18\sqrt{2}$$