Answer:
The square root of 3⁶/²⁵ is approximately 1.08.
Step-by-step explanation:
Break down the expression:
We can separate the radicals using the rule: √(a ^ b) = (√a) ^ b (square root of a to the power b equals bth root of a).
So, the expression becomes: √(3⁶) / √(²⁵)
Simplify the radicals:
√(3⁶) = 3^(⁶^1/²) = 3^(3) (since cube root of 3⁶ is 3 and 3 raised to the power 1 is simply 3).
√(²⁵) = 5^(²⁵^1/²) = 5^(2) (since fifth root of 25 is 5 and 5 raised to the power 1 is simply 5).
Divide the terms:
(3^(3)) / (5^(2)) = 27 / 25.
Note: It's not recommended to simplify 27/25 further as it's already in a relatively simple rational form. However, you can approximate the value to 1.08 using a calculator.
Therefore, the square root of 3⁶/²⁵ can be expressed as either 27/25 (exact form) or approximately 1.08 (decimal form).
