Simplify square root of s square root of s^7

Problem

√(,s(√(,s7())))

Solution

1. Rewrite the inner radical using a fractional exponent.

√(,s7())=s()(7/2)

2. Multiply the terms inside the outer radical by adding their exponents.

s⋅s(7/2)=s1⋅s()(7/2)

s(1+7/2)=s()(9/2)

3. Apply the outer square root as a fractional exponent.

√(,s()(9/2))=(s(9/2))(1/2)

4. Simplify the expression by multiplying the exponents.

(s(9/2))(1/2)=s()(9/4)

Final Answer

√(,s(√(,s7())))=s()(9/4)

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