square root of 145 simplified
Understand the Problem
The question is asking to simplify the square root of 145. To do this, we will look for perfect squares that can be factored out from 145 to simplify the expression.
Answer
The simplified form of the square root of 145 is \( \sqrt{145} \).
Answer for screen readers
The simplified form of the square root of 145 is ( \sqrt{145} ).
Steps to Solve
-
Identify perfect squares
First, we want to find any perfect squares that divide into 145. The perfect squares less than 145 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, and 144. The largest perfect square that divides 145 is 1 since 145 is not divisible by any larger perfect squares. -
Write the expression for simplification
This means we can express the square root of 145 as: $$ \sqrt{145} = \sqrt{1 \cdot 145} $$ -
Simplification
Since the only perfect square we have is 1, we can't simplify the square root further: $$ \sqrt{145} = \sqrt{145} $$ -
Final expression
Thus, the simplified form of the square root of 145 remains: $$ \sqrt{145} $$
The simplified form of the square root of 145 is ( \sqrt{145} ).
More Information
The square root of 145 cannot be simplified further because it does not contain any perfect square factors other than 1. This means that ( \sqrt{145} ) is an irrational number and can also be approximated as about 12.04 when calculated numerically.
Tips
- A common mistake is to try to simplify ( \sqrt{145} ) by assuming that it can be broken down into smaller integers. It is important to check for perfect square factors correctly.
AI-generated content may contain errors. Please verify critical information
