Simplify square root of s square root of s^3

Problem

√(,s(√(,s3())))

Solution

1. Rewrite the inner radical using a fractional exponent.

√(,s3())=s()(3/2)

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

s⋅s(3/2)=s1⋅s()(3/2)

s(1+3/2)=s()(5/2)

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

√(,s()(5/2))=(s(5/2))(1/2)

4. Simplify the expression by multiplying the exponents.

(s(5/2))(1/2)=s()(5/4)

Final Answer

√(,s(√(,s3())))=s()(5/4)

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