Simplify square root of x^7

Problem

√(,x^7)

Solution

1. Rewrite the radicand using a power that is a multiple of the index. Since the square root has an index of 2, we can write x^7 as x^6⋅x^1

2. Apply the product property of radicals, which states √(,a⋅b)=√(,a)⋅√(,b)

√(,x^7)=√(,x^6⋅x)

√(,x^7)=√(,x^6)⋅√(,x)

3. Simplify the perfect square term by dividing the exponent by the index.

√(,x^6)=x^(6/2)

√(,x^6)=x^3

4. Combine the simplified term with the remaining radical.

√(,x^7)=x^3√(,x)

Final Answer

√(,x^7)=x^3√(,x)

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