Solve sqrt{sqrt{55}*sqrt{275}*sqrt{605}}

$$\sqrt { \sqrt { 55 } \cdot \sqrt { 275 } \cdot \sqrt { 605 } }$$

Evaluate

$$55$$

Solution Steps

Factor 275=55\times 5. Rewrite the square root of the product \sqrt{55\times 5} as the product of square roots \sqrt{55}\sqrt{5}.

$$\sqrt{\sqrt{55}\sqrt{55}\sqrt{5}\sqrt{605}}$$

Multiply \sqrt{55} and \sqrt{55} to get 55.

$$\sqrt{55\sqrt{5}\sqrt{605}}$$

Factor 605=5\times 121. Rewrite the square root of the product \sqrt{5\times 121} as the product of square roots \sqrt{5}\sqrt{121}.

$$\sqrt{55\sqrt{5}\sqrt{5}\sqrt{121}}$$

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

$$\sqrt{55\times 5\sqrt{121}}$$

Multiply 55 and 5 to get 275.

$$\sqrt{275\sqrt{121}}$$

Calculate the square root of 121 and get 11.

$$\sqrt{275\times 11}$$

Multiply 275 and 11 to get 3025.

$$\sqrt{3025}$$

Calculate the square root of 3025 and get 55.

$$55$$

Factor

$$5\times 11$$