Square roots, step by step
A square root asks which number, multiplied by itself, gives this one.
The question
√289
√289=▢
10²=100— under
20²=400— over
√289is between10 and 20
√289=13 or 17
√289=17
17 × 17=289
√289=17
- √ asks a question: which number times itself gives 289? It is not an instruction to halve 289 — that is the mistake this symbol collects.
- Bracket it first. 10² = 100, which is under 289, and 20² = 400, which is over. So the answer is between 10 and 20.
- Now the last digit. 289 ends in 9, and the only digits whose square ends in 9 are 3 and 7. Between 10 and 20 that leaves 13 or 17.
- Two left, and the bracket picks between them: 289 is nearer 400 than 100, so take the bigger one — 17.
- Check it: 17 × 17 = 289. So √289 = 17.
How it works.
- 01
√ asks a question: which number times itself gives 289? It is not an instruction to halve 289 — that is the mistake this symbol collects.
- 02
Bracket it first. 10² = 100, which is under 289, and 20² = 400, which is over. So the answer is between 10 and 20.
- 03
Now the last digit. 289 ends in 9, and the only digits whose square ends in 9 are 3 and 7. Between 10 and 20 that leaves 13 or 17.
- 04
Two left, and the bracket picks between them: 289 is nearer 400 than 100, so take the bigger one — 17.
- 05
Check it: 17 × 17 = 289. So √289 = 17.