Square root of 147
Understand the Problem
The question is asking to calculate the square root of the number 147, which requires mathematical reasoning to simplify or estimate.
Answer
Approximately 12.124
Answer for screen readers
The final answer is approximately 12.124
Steps to Solve
Steps to Solve the Problem of Finding the Square Root of 147
- Factorize the number 147
We first find the prime factorization of 147.
$147 = 3 imes 49 = 3 imes 7 imes 7 = 3 imes 7^2$
- Separate and simplify the square root
Using the property of square roots that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can simplify the square root of the prime factors.
$\sqrt{147} = \sqrt{3 \times 7^2} = \sqrt{3} \times \sqrt{7^2}$
Since $\sqrt{7^2} = 7$, this simplifies to:
$\sqrt{147} = \sqrt{3} \times 7$
- Estimate the square root of 3
We can approximate $\sqrt{3} \approx 1.732$. Therefore,
$\sqrt{147} \approx 1.732 \times 7 = 12.124$
The final answer is approximately 12.124
More Information
The square root of 147 does not result in an integer, so it is typically represented in simplified radical form or as an approximation.
Tips
A common mistake is not simplifying the radical completely or incorrectly estimating the square root of 3. Always double-check your factorization and estimation.