Determine square roots of perfect squares

Perfect squares are nonnegative integers that result from multiplying a whole number by itself; determining their square roots involves identifying that factor and interpreting the square-root operation as the inverse of squaring. The symbol √ denotes the principal, nonnegative root, while an equation such as $x^2=49$ has two integer solutions, $x=7$ and $x=-7$ ; this scope excludes approximating non-perfect-square roots and more advanced radical operations.

Detailed Explanation: Determine square roots of perfect squares

A perfect square is a whole number made by multiplying a whole number by itself. For example,

7 \times 7=49,

so $49$ is a perfect square.

The symbol $\sqrt{\phantom{x}}$ asks: “What nonnegative number was multiplied by itself to make this number?”

Example: Find $\sqrt{49}$

Think of a number multiplied by itself that equals $49$ :

7 \times 7=49.

Therefore, the number whose square is $49$ is $7$ :

\sqrt{49}=7.

The square-root symbol means the principal root, which is the nonnegative root. So $\sqrt{49}$ is $7$ , not $\pm 7$ .

However, if the problem asks you to solve an equation such as

x^2=49,

then both $7$ and $-7$ work because

7^2=49 \quad \text{and} \quad (-7)^2=49.

Thus, the solutions to $x^2=49$ are $x=7$ and $x=-7$ .

Learn by doing: Determine square roots of perfect squares

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Square Roots of Perfect Squares From Equation

Earned ?