Evaluate fourth root of 5^2

Problem

√(4,5^2)

Solution

1. Rewrite the radical expression using a fractional exponent.

√(4,5^2)=(5^2)^1/4

2. Apply the power of a power rule, which states that (a^m)^n=a^(m⋅n)

(5^2)^1/4=5^(2⋅1/4)

3. Simplify the exponent by multiplying the fraction.

5^(2⋅1/4)=5^2/4

4. Reduce the fraction in the exponent to its simplest form.

5^2/4=5^1/2

5. Convert the expression back into radical form.

5^1/2=√(,5)

Final Answer

√(4,5^2)=√(,5)

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