Simplify square root of s square root of s^4

Problem

√(,s(√(,s4())))

Solution

1. Simplify the inner radical by taking the square root of s4()

√(,s4())=s2()

2. Substitute the simplified inner expression back into the original radical.

√(,s⋅s2())

3. Combine the terms inside the radical using the product rule for exponents, s1⋅s2=s()(1+2)

√(,s3())

4. Rewrite the radical using a fractional exponent, where √(,x)=x(1/2)

(s3)(1/2)

5. Apply the power rule for exponents, (am)n=a(m⋅n) to find the final simplified form.

s()(3/2)

Final Answer

√(,s(√(,s4())))=s()(3/2)

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