square root of 147 in radical form
Understand the Problem
The question is asking for the square root of 147 expressed in radical form. To solve this, we will look for any perfect square factors of 147 that can be extracted from the square root.
Answer
\( 7\sqrt{3} \)
Answer for screen readers
The square root of 147 in radical form is ( 7\sqrt{3} ).
Steps to Solve
- Find the factors of 147
First, we need to determine the factors of 147. The prime factorization of 147 is as follows.
147 can be divided by 3 and 49, so: $$ 147 = 3 \times 49 $$
Next, we notice that 49 is a perfect square: $$ 49 = 7^2 $$
- Express 147 in terms of its square roots
Now that we have the prime factorization, we can express $\sqrt{147}$ as follows: $$ \sqrt{147} = \sqrt{3 \times 49} $$
- Extract the perfect square
Since 49 is a perfect square, we can simplify the square root: $$ \sqrt{147} = \sqrt{3} \times \sqrt{49} = \sqrt{3} \times 7 $$
- Final expression in radical form
Thus, the simplified radical form of $\sqrt{147}$ is: $$ \sqrt{147} = 7\sqrt{3} $$
The square root of 147 in radical form is ( 7\sqrt{3} ).
More Information
The number 147 is not a perfect square itself, but it can be simplified by factoring out its perfect square component, which is 49 in this case. This method of simplifying square roots can help in various math problems, especially in algebra.
Tips
A common mistake is to stop at finding the prime factorization and not extract the perfect square part from the square root. Always ensure to look for and extract any perfect squares to simplify the expression completely.