147 square root simplified
Understand the Problem
The question is asking how to simplify the square root of 147. This involves identifying perfect square factors of 147 and simplifying the expression accordingly.
Answer
$7\sqrt{3}$
Answer for screen readers
The final answer is $7\sqrt{3}$.
Steps to Solve
- Identify the factors of 147
First, we need to find the prime factorization of 147 to identify any perfect square factors. The prime factors of 147 are:
$$ 147 = 3 \times 49 $$
Since (49) is a perfect square ((7^2)), we can use it to simplify the square root.
- Set up the square root expression
Now that we've identified a perfect square, we can set up the square root expression:
$$ \sqrt{147} = \sqrt{3 \times 49} $$
- Simplify the square root
Next, we can simplify the square root using the property of square roots that states ( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} ):
$$ \sqrt{147} = \sqrt{3} \times \sqrt{49} $$
Since ( \sqrt{49} = 7 ), we can simplify further:
$$ \sqrt{147} = \sqrt{3} \times 7 = 7\sqrt{3} $$
- Write the final simplified form
The final simplified form of the square root of 147 is:
$$ \sqrt{147} = 7\sqrt{3} $$
The final answer is $7\sqrt{3}$.
More Information
The value $7\sqrt{3}$ is the simplest form of the square root of 147. Simplifying square roots can help in various mathematical applications, including solving equations and integrating functions in calculus.
Tips
- Forgetting to factor completely or missing a perfect square factor.
- Not recognizing that $49$ is a perfect square, leading to incorrect simplification.
- Confusing the product of square roots, such as ( \sqrt{3} \times \sqrt{49} ).
