What Are the Square Roots of 16?

The exact square roots of 16 are 4 and -4.

Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms, if y is the square root of x, then y * y = x, or y² = x.

Most positive numbers have two square roots: one positive and one negative. This is because a positive number squared (y * y) results in a positive number, and a negative number squared (-y * -y) also results in a positive number.

The Square Roots of 16

To find the square roots of 16, we are looking for the number(s) that satisfy the equation:

x² = 16

There are two solutions to this equation:

1. Positive Square Root: When x is positive, 4 * 4 = 16. According to the reference, the square root of 16 is 4. It is specifically the positive solution of the equation x² = 16.
2. Negative Square Root: When x is negative, -4 * -4 = 16. So, -4 is also a square root of 16.

Therefore, the square roots of 16 are 4 and -4.

Key Points

• A number n has two square roots: √n (the principal, or positive, square root) and -√n (the negative square root).
• For 16, the positive square root is √16 = 4.
• The negative square root is -√16 = -4.
• The number 16 is considered a perfect square because its square roots (4 and -4) are integers.

Visualizing the Square Roots

We can represent the relationship like this:

Number	Square Root(s)	Equation
16	4	4 * 4 = 16
16	-4	(-4) * (-4) = 16

Understanding both positive and negative square roots is crucial when solving equations involving squares.