Question
Use a calculator to solve the equation below. Use pencil and paper. Before computing anything, write down two perfect squares you know, one that is less than the given number and one that is greater than the given number. Then write down their square roots as two numbers you know b must be between.
bsquaredequals175
Question content area bottom
Part 1
balmost equals
enter your response here
(Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
bsquaredequals175
Question content area bottom
Part 1
balmost equals
enter your response here
(Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
Answers
GPT-4o mini
To solve the equation \( b^2 = 175 \), we can start by identifying two perfect squares that are close to 175.
1. A perfect square less than 175: \( 144 \) (which is \( 12^2 \))
2. A perfect square greater than 175: \( 196 \) (which is \( 14^2 \))
Now, we know that:
- The square root of \( 144 \) is \( 12 \)
- The square root of \( 196 \) is \( 14 \)
This tells us:
\[
12 < b < 14
\]
Next, we'll compute the square root of \( 175 \):
Using a calculator:
\[
b = \sqrt{175} \approx 13.22876
\]
Now, we round \( b \) to the nearest tenth:
\[
b \approx 13.2
\]
### Final Answer:
The value of \( b \) is approximately \( 13.2 \).
1. A perfect square less than 175: \( 144 \) (which is \( 12^2 \))
2. A perfect square greater than 175: \( 196 \) (which is \( 14^2 \))
Now, we know that:
- The square root of \( 144 \) is \( 12 \)
- The square root of \( 196 \) is \( 14 \)
This tells us:
\[
12 < b < 14
\]
Next, we'll compute the square root of \( 175 \):
Using a calculator:
\[
b = \sqrt{175} \approx 13.22876
\]
Now, we round \( b \) to the nearest tenth:
\[
b \approx 13.2
\]
### Final Answer:
The value of \( b \) is approximately \( 13.2 \).