Solve 12sqrt{45}-8sqrt{80}

$$12 \sqrt { 45 } - 8 \sqrt { 80 }$$

Evaluate

$$4\sqrt{5}\approx 8.94427191$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$12\times 3\sqrt{5}-8\sqrt{80}$$

Multiply 12 and 3 to get 36.

$$36\sqrt{5}-8\sqrt{80}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$36\sqrt{5}-8\times 4\sqrt{5}$$

Multiply -8 and 4 to get -32.

$$36\sqrt{5}-32\sqrt{5}$$

Combine 36\sqrt{5} and -32\sqrt{5} to get 4\sqrt{5}.

$$4\sqrt{5}$$