worldofcalcsSquare Root Calculator 📐
√72
8.48528137
Simplified: √72 = 6√2
What is a square root?
The square root of a number is the value that, multiplied by itself, gives that number: √64 = 8 because 8 × 8 = 64. This calculator gives the decimal value and, for whole numbers, the simplified surd form you need in exams, such as √72 = 6√2.
Simplifying a square root
√(a² × b) = a√b
Factorise the number into primes and pair up equal factors. Each pair comes out of the root as one factor; anything unpaired stays inside. If everything pairs up, the number is a perfect square.
Good to know
- Perfect squares up to 400: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400.
- Negative numbers have no real square root; their roots are imaginary numbers.
- √2 ≈ 1.414, √3 ≈ 1.732 and √5 ≈ 2.236 are worth remembering.
- To estimate a root, find the perfect squares on either side: √50 is a little over 7, since 7² = 49.
Worked example
- Simplify √72
- 72 = 2 × 2 × 2 × 3 × 3
- The pairs (2 × 2) and (3 × 3) come out as 2 × 3 = 6; one 2 is left inside
- √72 = 6√2 ≈ 8.4853
Square roots and simplified forms
Common square roots to four decimal places.
| Number | Simplified | Value |
|---|---|---|
| √2 | — | 1.4142 |
| √3 | — | 1.7321 |
| √5 | — | 2.2361 |
| √8 | 2√2 | 2.8284 |
| √12 | 2√3 | 3.4641 |
| √18 | 3√2 | 4.2426 |
| √20 | 2√5 | 4.4721 |
| √50 | 5√2 | 7.0711 |
| √72 | 6√2 | 8.4853 |
| √98 | 7√2 | 9.8995 |
Numbers with no square factor can't be simplified.