Square root of 66 simplified
Understand the Problem
The question is asking for the simplified form of the square root of 66. This requires identifying any perfect square factors of 66 and simplifying the square root accordingly.
Answer
$ \sqrt{66} \approx 8.124 $
Answer for screen readers
The simplified form of the square root of 66 is $ \sqrt{66} $, and its approximate decimal value is $ 8.124 $.
Steps to Solve
- Identify the factors of 66
First, we need to find the factors of 66. The prime factorization of 66 is obtained by dividing it by its prime factors. $$ 66 = 2 \times 3 \times 11 $$
- Check for perfect square factors
Next, we look for any perfect square factors among the prime factors. The prime factors of 66 are 2, 3, and 11, none of which are perfect squares.
- State the radical form
Since there are no perfect square factors, the square root of 66 stays in its radical form: $$ \sqrt{66} $$
- Provide the approximate decimal value
For practical purposes, we can also express $\sqrt{66}$ as an approximate decimal value using a calculator: $$ \sqrt{66} \approx 8.124 $$
The simplified form of the square root of 66 is $ \sqrt{66} $, and its approximate decimal value is $ 8.124 $.
More Information
The square root of 66 cannot be simplified further because it has no perfect squares as factors. Its approximate value, $ 8.124 $, can help in practical applications where an estimation is needed.
Tips
- One common mistake is assuming that $ \sqrt{66} $ can be simplified further without recognizing the absence of perfect square factors. Always check for perfect squares before concluding.
