Question
Help me out 9/4 is close to the square root of what integer? (1 Point)
Answers
GPT-4o mini
To find the integer that is close to the square of \( \frac{9}{4} \), we first calculate \( \left( \frac{9}{4} \right)^2 \).
\[
\left( \frac{9}{4} \right)^2 = \frac{9^2}{4^2} = \frac{81}{16}
\]
Now we can convert \( \frac{81}{16} \) into a decimal:
\[
\frac{81}{16} = 5.0625
\]
Thus, \( \frac{9}{4} \) is close to the square root of \( 5.0625 \), which means it is also close to:
\[
\sqrt{81} = 9
\]
The integer that \( \frac{9}{4} \) is close to the square root of is 5, because \( \sqrt{5.0625} \) is about \( \frac{9}{4} \).
So the answer is:
**5**
\[
\left( \frac{9}{4} \right)^2 = \frac{9^2}{4^2} = \frac{81}{16}
\]
Now we can convert \( \frac{81}{16} \) into a decimal:
\[
\frac{81}{16} = 5.0625
\]
Thus, \( \frac{9}{4} \) is close to the square root of \( 5.0625 \), which means it is also close to:
\[
\sqrt{81} = 9
\]
The integer that \( \frac{9}{4} \) is close to the square root of is 5, because \( \sqrt{5.0625} \) is about \( \frac{9}{4} \).
So the answer is:
**5**