Square root
The square root of a number is the value that, when multiplied by itself, gives that number. The square root symbol is √. For example, √36 = 6 because 6 × 6 = 36, and √81 = 9 because 9 × 9 = 81. Introduced in Saxon Math Intermediate 4, this 4th grade math concept connects directly to multiplication facts students already know and builds toward geometry — the side length of a square with area 81 sq in is √81 = 9 inches.
Key Concepts
Property To find the square root of a number, we find a number that, when multiplied by itself, equals the original number. We use the symbol $\sqrt{\phantom{x}}$ to indicate the square root.
Examples The square root of 36 is 6, because $6 \times 6 = 36$, written as $\sqrt{36}=6$. A square with area 81 sq. in. has a side length of $\sqrt{81}=9$ in.
Explanation Think of square root as the 'undo' button for squaring. If you have the area of a perfect square, the square root reveals the length of one side. A square garden with 49 flowers has sides that are $\sqrt{49} = 7$ flowers long. It’s finding the base of the square.
Common Questions
What is a square root in math?
A square root of a number is the value that, multiplied by itself, equals that number. For example, the square root of 25 is 5 because 5 × 5 = 25. The symbol for square root is √, so √25 = 5.
How do you find the square root of a perfect square?
Think of your multiplication facts: which number times itself gives the number under the √ symbol? For √64, ask 'what times itself is 64?' — the answer is 8, so √64 = 8.
What is a perfect square?
A perfect square is a whole number whose square root is also a whole number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 are all perfect squares because their roots are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
How does square root connect to geometry?
If you know the area of a square, the side length is the square root of the area. A square with area 49 sq cm has side length √49 = 7 cm. This is why the operation is called 'square' root.
When do students learn about square roots?
Square roots are introduced in 4th grade in Saxon Math Intermediate 4 as an extension of multiplication facts. Students deepen this understanding in middle school when they study irrational numbers and the Pythagorean theorem.
What are common mistakes when finding square roots?
A common mistake is confusing square root with dividing by 2. √16 = 4 (not 8). Another error is thinking every number has a whole-number square root — most numbers do not have exact whole-number roots.