To find the equivalent expression to [tex]\( 25^{\frac{1}{2}} \)[/tex], we need to analyze and simplify each option proposed in the question.
Given that [tex]\( 25^{\frac{1}{2}} \)[/tex] is equal to the square root of 25:
[tex]\[ 25^{\frac{1}{2}} = \sqrt{25} \][/tex]
The square root of 25 is 5:
[tex]\[ \sqrt{25} = 5 \][/tex]
Now, let's evaluate each option given:
1. [tex]\( 25 - \frac{2}{7} \)[/tex]:
This expression represents a subtraction problem:
[tex]\[ 25 - \frac{2}{7} \][/tex]
This is clearly not 5.
2. [tex]\( 25 - \frac{7}{2} \)[/tex]:
Again, this is a subtraction problem:
[tex]\[ 25 - \frac{7}{2} \][/tex]
This will also not result in 5.
3. [tex]\( \sqrt[7]{25^2} \)[/tex]:
This expression represents the seventh root of 25 squared:
[tex]\[ \sqrt[7]{25^2} = (25^2)^{\frac{1}{7}} = 25^{\frac{2}{7}} \][/tex]
This does not simplify to 5.
4. [tex]\( \sqrt{25^7} \)[/tex]:
This can be simplified as follows:
[tex]\[ \sqrt{25^7} = (25^7)^{\frac{1}{2}} = 25^{(7 \times \frac{1}{2})} = 25^{\frac{7}{2}} \][/tex]
This does not simplify to 5.
Given the detailed analysis, we conclude that none of the options are equivalent to:
[tex]\[ 25^{\frac{1}{2}} = \sqrt{25} = 5 \][/tex]
However, there appears to be no correct matching option among the given choices based on the analysis provided. It seems there might be an issue with the options listed in relation to the correct answer derived, [tex]\(25^{\frac{1}{2}} = 5\)[/tex].
