Square Root Chart (1–25)
A quick reference for the most commonly needed square roots. Perfect squares are shown in green.
How to Find a Square Root
The square root of a number N is the value that when multiplied by itself equals N. Written as √N or N^½, every positive number has two square roots — one positive and one negative — but we always use the positive (principal) root.
Method 1 — Perfect squares (easiest)
If the number is a perfect square (1, 4, 9, 16, 25…), the answer is a whole number. Memorise the first 15: √1=1, √4=2, √9=3, √16=4, √25=5, √36=6, √49=7, √64=8, √81=9, √100=10, √121=11, √144=12, √169=13, √196=14, √225=15.
Method 2 — Estimation for non-perfect squares
Find the two perfect squares the number falls between. For √50: it falls between √49=7 and √64=8. Start with 7.1, square it: 7.1²=50.41. Too high. Try 7.07: 7.07²=49.98 ≈ 50. So √50 ≈ 7.07.
Method 3 — Calculator formula
Any number raised to the power of ½ gives its square root. √N = N^0.5. On a calculator: enter the number, press the √ key or use the exponent key and enter 0.5.
Square Root Laws
These rules govern how square roots behave in equations. Knowing them makes simplifying expressions much faster.
- Product rule: √(a × b) = √a × √b → √(4×9) = √4 × √9 = 2 × 3 = 6
- Quotient rule: √(a ÷ b) = √a ÷ √b → √(100÷4) = √100 ÷ √4 = 10 ÷ 2 = 5
- Power rule: √(a²) = a → √(7²) = 7
- Addition: √a + √b ≠ √(a+b) → you cannot combine unlike square roots
- Negative: √(−a) is not real — it equals i√a (imaginary)
- Zero: √0 = 0
Frequently Asked Questions
What is the square root of 2?
√2 ≈ 1.41421356. It is irrational — it cannot be written as a fraction. Full solution →
What is the square root of a negative number?
Negative numbers have no real square root. √−1 = i (imaginary unit). Learn more →
Is the square root of 0 a real number?
Yes. √0 = 0, which is a real number. Learn more →
What does the square root function look like?
The graph of y = √x starts at (0,0) and curves upward to the right, getting flatter as x increases. It only exists for x ≥ 0. See the graph →
What is the easiest way to find a square root?
For perfect squares, memorise the table 1–15. For others, use the estimation method or a calculator. Full guide →