Square Roots 1-100
REFSquare Root Table
| n | √n | n | √n | n | √n | n | √n |
|---|
Perfect Squares (1-100)
| n² | n | √(n²) |
|---|---|---|
| 1 | 1² | 1 |
| 4 | 2² | 2 |
| 9 | 3² | 3 |
| 16 | 4² | 4 |
| 25 | 5² | 5 |
| 36 | 6² | 6 |
| 49 | 7² | 7 |
| 64 | 8² | 8 |
| 81 | 9² | 9 |
| 100 | 10² | 10 |
Square Root Rules
√(a × b) = √a × √b
Product rule: Square root of a product equals product of square roots
√(a / b) = √a / √b
Quotient rule: Square root of a quotient equals quotient of square roots
√(a²) = |a|
Square root of a perfect square equals the absolute value
(√a)² = a
Squaring a square root returns the original number
Understanding Square Roots
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √16 = 4 because 4 × 4 = 16. Perfect squares (1, 4, 9, 16, 25...) have whole number square roots. Other numbers have irrational square roots with infinite decimal places. Square roots are used in geometry, algebra, physics, and engineering calculations.
Frequently Asked Questions
What is the value of √2?
√2 is irrational and approximately 1.414. It cannot be written as an exact fraction, and its decimal never ends or repeats. Other common irrational roots include √3 ≈ 1.732 and √5 ≈ 2.236.
Can a negative number have a square root?
Not within the real numbers, because any real number squared is zero or positive. Square roots of negatives require imaginary numbers, where √(-1) is defined as i.
How can I estimate a square root without a calculator?
Find the two nearest perfect squares. For √50, note 49 = 7² and 64 = 8², so √50 is just above 7 (about 7.07). The closer the number is to a perfect square, the closer the root is to that whole number.