Solve 3sqrt{10}*6sqrt{5}+sqrt{288}-45sqrt{2}

$$3 \sqrt{ 10 } \times 6 \sqrt{ 5 } + \sqrt{ 288 } -45 \sqrt{ 2 }$$

Evaluate

$$57\sqrt{2}\approx 80.610173055$$

Solution Steps

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$3\times 6\sqrt{5}\sqrt{2}\sqrt{5}+\sqrt{288}-45\sqrt{2}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$3\times 6\times 5\sqrt{2}+\sqrt{288}-45\sqrt{2}$$

Multiply 3 and 6 to get 18.

$$18\times 5\sqrt{2}+\sqrt{288}-45\sqrt{2}$$

Multiply 18 and 5 to get 90.

$$90\sqrt{2}+\sqrt{288}-45\sqrt{2}$$

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}.

$$90\sqrt{2}+12\sqrt{2}-45\sqrt{2}$$

Combine 90\sqrt{2} and 12\sqrt{2} to get 102\sqrt{2}.

$$102\sqrt{2}-45\sqrt{2}$$

Combine 102\sqrt{2} and -45\sqrt{2} to get 57\sqrt{2}.

$$57\sqrt{2}$$