arithmetic
What is a Square Root?
⚡ THE DEFINITION
The square root of a number is a value that, when multiplied by itself, gives the original number.
√x = y ⇔ y² = x← THE DEFINITION
Introduction to Square Roots
A square root goes in the 'opposite' direction of squaring a number. If you know that 5 squared (5²) is 25, then the square root of 25 (√25) is 5.
How to Find a Square Root
1
Think of Squares
Ask yourself: What number times itself equals the target?
2
Identify Perfect Squares
Numbers like 4, 9, 16, 25 are perfect squares because their roots are whole numbers.
3
Use the Symbol
The symbol for square root is called the radical sign: √.
Perfect Squares to Memorize
√4 = 22 × 2 = 4
√9 = 33 × 3 = 9
√16 = 44 × 4 = 16
√25 = 55 × 5 = 25
√100 = 1010 × 10 = 100
💡Expert Tips
- Negative numbers do not have real square roots (you can't multiply a real number by itself to get a negative).
- Every positive number actually has two square roots: a positive and a negative (e.g., 5 and -5 both square to 25). Usually, we use the positive one called the 'Principal Square Root'.
- The square root of a square returns the original absolute value: √(x²) = |x|.