To determine which of the options is a rational number between 5 and \( 5 \frac{1}{4} \) (or 5.25), let's evaluate each choice:
-
Square root of 26:
\( \sqrt{26} \) is approximately 5.099. This is between 5 and 5.25. -
\( 5 \frac{1}{8} \):
This is equal to \( 5 + 0.125 = 5.125 \), which is also between 5 and 5.25. -
\( 5 \frac{2}{5} \):
This is equal to \( 5 + 0.4 = 5.4 \), which is greater than 5.25. -
\( 5 \frac{1}{3} \):
This is equal to \( 5 + \frac{1}{3} \approx 5.333 \), which is also greater than 5.25.
Based on this analysis, the rational numbers that fall between 5 and \( 5 \frac{1}{4} \) are:
- Square root of 26
- \( 5 \frac{1}{8} \)
So, both \( \sqrt{26} \) and \( 5 \frac{1}{8} \) are rational numbers between 5 and \( 5 \frac{1}{4} \).