To calculate \( 36 \) to the square root of \( 12 \) mathematically, you'll first find \( \sqrt{12} \) and then raise \( 36 \) to that power:
-
Calculate \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
-
Now, calculate \( 36^{\sqrt{12}} \): \[ 36^{\sqrt{12}} = 36^{2\sqrt{3}} \]
Since \( 36 = 6^2 \), this can also be rewritten as: \[ (6^2)^{2\sqrt{3}} = 6^{4\sqrt{3}} \]
Thus, \( 36 \) to the square root of \( 12 \) is:
\[ 36^{\sqrt{12}} = 6^{4\sqrt{3}} \]
If you want a numerical approximation, you can compute:
- \( \sqrt{12} \approx 3.464 \)
- Then \( 36^{3.464} \approx 10305.21 \) (using a calculator).
So, \( 36^{\sqrt{12}} \) can be expressed as \( 6^{4\sqrt{3}} \) or approximated numerically as around \( 10305.21 \).