Simplify square root of y^13

Problem

√(,y13)

Solution

1. Rewrite the radicand using the properties of exponents to isolate the largest even power, since √(,yn)=y(n/2) for even n

√(,y12⋅y)

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

√(,y12)⋅√(,y)

3. Simplify the square root of the even power by dividing the exponent by 2.

y6√(,y)

Final Answer

√(,y13)=y6√(,y)

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