What is the square root of 152?
Understand the Problem
The question is asking for the square root of the number 152. To solve this, we will calculate the value that, when multiplied by itself, equals 152.
Answer
$$ \sqrt{152} \approx 12.33 $$
Answer for screen readers
$$ \sqrt{152} \approx 12.33 $$
Steps to Solve
- Identify the number for square root calculation
We need to find the square root of 152. This is represented as $\sqrt{152}$.
- Estimate the square root
To estimate the square root of 152, we find two perfect squares that surround 152.
For example:
- $12^2 = 144$
- $13^2 = 169$
Therefore, $\sqrt{152}$ is between 12 and 13.
- Use a calculator or simplify further
Using a calculator gives: $$ \sqrt{152} \approx 12.3288 $$
We can also express 152 in its prime factorization and simplify. 152 can be factored into $4 \times 38$ or $4 \times 4 \times 9.5$, etc.
- State the decimal value and its approximation
So the approximate square root of 152 is $12.33$ rounded to two decimal places.
$$ \sqrt{152} \approx 12.33 $$
More Information
The number 152 is not a perfect square, but its square root can be expressed in decimal form, approximately $12.33$. This means if you multiply $12.33$ by itself, you will get a value close to $152$. Square roots are commonly used in various mathematical applications, including geometry, algebra, and trigonometry.
Tips
- Rounding too early: It’s important to keep extra decimal places during calculations and only round off at the final answer.
- Not identifying perfect squares: Make sure to find the perfect squares surrounding the number to help with estimation.
