To express \( 24 \frac{1}{4} \) using a root, we first convert the mixed number to an improper fraction.
The mixed number \( 24 \frac{1}{4} \) can be converted as follows:
-
Multiply the whole number (24) by the denominator (4):
\( 24 \times 4 = 96 \) -
Add the numerator (1) to this result:
\( 96 + 1 = 97 \)
So, \( 24 \frac{1}{4} \) can be written as the improper fraction \( \frac{97}{4} \).
Next, let's express \( 24 \frac{1}{4} \) as a square root by writing it as:
\[ \sqrt{(24 \frac{1}{4})^2} = \sqrt{(24.25)^2} = \sqrt{\left(\frac{97}{4}\right)^2} \]
Thus, \( 24 \frac{1}{4} \) can be expressed with a square root as:
\[ \sqrt{\left(\frac{97}{4}\right)^2} \]
Therefore, \( 24 \frac{1}{4} = \sqrt{(24 \frac{1}{4})^2} \).
Alternatively, you could express \( 24 \frac{1}{4} \) as \( \frac{\sqrt{97^2}}{2} \) if you simplify \( \frac{97}{4} \) further.