the area of a square can be represented by the expression x10. which monomial represents a side of the square?
The area of a square can be represented by the expression ( x^{10} ). Which monomial represents a side of the square?
Answer: To determine which monomial represents a side of the square when the area is given by the expression ( x^{10} ), we need to recall the relationship between the side length and the area of a square.
The area ( A ) of a square is given by the formula:
A = s^2
where ( s ) is the side length of the square.
Given that the area ( A ) is ( x^{10} ), we can set up the equation:
s^2 = x^{10}
To find ( s ), we take the square root of both sides of the equation:
s = \sqrt{x^{10}}
Using the property of exponents that ( \sqrt{x^n} = x^{n/2} ), we get:
s = x^{10/2}
s = x^5
Therefore, the monomial that represents a side of the square is ( \boxed{x^5} ).