Simplify square root of x^10

Problem

√(,x10)

Solution

1. Identify the index of the radical and the exponent of the radicand. The square root has an index of 2 and the radicand is x10

2. Apply the rule for simplifying radicals with exponents, which states √(n,am)=am/n

3. Divide the exponent by the index to simplify the expression.

10/2=5

4. Simplify the expression by writing the base with the new exponent. Since the index is even and the resulting exponent is odd, we use absolute value bars to ensure the result is non-negative if x is a real number.

√(,x10)=|x|5

Final Answer

√(,x10)=|x|5

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