Question
I'm studying for my math exam and I need help with a problem involving geometric mean. Can you find the value of x when the two numbers are 4 and 6, rounded to the nearest tenth?
Answers
GPT-4o mini
To find the geometric mean of two numbers, you can use the formula:
\[
\text{Geometric Mean} = \sqrt{a \times b}
\]
where \( a \) and \( b \) are the two numbers. In your case, the two numbers are 4 and 6.
Let's calculate it:
1. Multiply the two numbers:
\[
4 \times 6 = 24
\]
2. Take the square root of the result:
\[
\sqrt{24}
\]
3. Simplifying \(\sqrt{24}\):
\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\]
4. To get a numerical value for \(\sqrt{6}\), we can approximate it:
\[
\sqrt{6} \approx 2.44949
\]
Therefore:
\[
2\sqrt{6} \approx 2 \times 2.44949 \approx 4.89898
\]
5. Rounding this value to the nearest tenth:
\[
4.9
\]
Thus, the geometric mean of 4 and 6, rounded to the nearest tenth, is approximately **4.9**.
\[
\text{Geometric Mean} = \sqrt{a \times b}
\]
where \( a \) and \( b \) are the two numbers. In your case, the two numbers are 4 and 6.
Let's calculate it:
1. Multiply the two numbers:
\[
4 \times 6 = 24
\]
2. Take the square root of the result:
\[
\sqrt{24}
\]
3. Simplifying \(\sqrt{24}\):
\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\]
4. To get a numerical value for \(\sqrt{6}\), we can approximate it:
\[
\sqrt{6} \approx 2.44949
\]
Therefore:
\[
2\sqrt{6} \approx 2 \times 2.44949 \approx 4.89898
\]
5. Rounding this value to the nearest tenth:
\[
4.9
\]
Thus, the geometric mean of 4 and 6, rounded to the nearest tenth, is approximately **4.9**.