Simplify

Problem

√(7,256*x8)/√(7,2*x)

Solution

1. Apply the quotient property of radicals to combine the numerator and denominator into a single seventh root.

√(7,(256*x8)/(2*x))

2. Simplify the fraction inside the radical by dividing the coefficients and subtracting the exponents of the variable x

256/2=128

x8÷x=x7

√(7,128*x7)

3. Rewrite the radicand to identify perfect seventh powers, noting that 128=2

√(7,2⋅x7)

4. Extract the seventh roots of the terms inside the radical.

√(7,2)⋅√(7,x7)=2*x

Final Answer

√(7,256*x8)/√(7,2*x)=2*x

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