Solve sqrt{2}*sqrt{3}*sqrt{5}*sqrt{12}*sqrt{45}*sqrt{50}

$$\sqrt { 2 } \times \sqrt { 3 } \times \sqrt { 5 } \times \sqrt { 12 } \times \sqrt { 45 } \times \sqrt { 50 }$$

Evaluate

$$900$$

Solution Steps

Factor 12=2\times 6. Rewrite the square root of the product \sqrt{2\times 6} as the product of square roots \sqrt{2}\sqrt{6}.

$$\sqrt{2}\sqrt{3}\sqrt{5}\sqrt{2}\sqrt{6}\sqrt{45}\sqrt{50}$$

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

$$2\sqrt{3}\sqrt{5}\sqrt{6}\sqrt{45}\sqrt{50}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$2\sqrt{3}\sqrt{5}\sqrt{3}\sqrt{2}\sqrt{45}\sqrt{50}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 3\sqrt{5}\sqrt{2}\sqrt{45}\sqrt{50}$$

Factor 45=5\times 9. Rewrite the square root of the product \sqrt{5\times 9} as the product of square roots \sqrt{5}\sqrt{9}.

$$2\times 3\sqrt{5}\sqrt{2}\sqrt{5}\sqrt{9}\sqrt{50}$$

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

$$2\times 3\times 5\sqrt{2}\sqrt{9}\sqrt{50}$$

Factor 50=2\times 25. Rewrite the square root of the product \sqrt{2\times 25} as the product of square roots \sqrt{2}\sqrt{25}.

$$2\times 3\times 5\sqrt{2}\sqrt{9}\sqrt{2}\sqrt{25}$$

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

$$2\times 3\times 5\times 2\sqrt{9}\sqrt{25}$$

Multiply 2 and 3 to get 6.

$$6\times 5\times 2\sqrt{9}\sqrt{25}$$

Multiply 6 and 5 to get 30.

$$30\times 2\sqrt{9}\sqrt{25}$$

Multiply 30 and 2 to get 60.

$$60\sqrt{9}\sqrt{25}$$

Calculate the square root of 9 and get 3.

$$60\times 3\sqrt{25}$$

Multiply 60 and 3 to get 180.

$$180\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$180\times 5$$

Multiply 180 and 5 to get 900.

$$900$$

Factor

$$2^{2}\times 3^{2}\times 5^{2}$$