Square roots and cube roots
The question
√784
√784=▢
20²=400— under
30²=900— over
√784is between20 and 30
√784=22 or 28
√784=28
28 × 28=784
√784=28
- √ asks a question: which number times itself gives 784? It does not mean half of 784.
- Bracket it first. 20² = 400, which is under 784, and 30² = 900, which is over. So the answer is between 20 and 30.
- Now the last digit. 784 ends in 4, and the only digits whose square ends in 4 are 2 and 8. Between 20 and 30 that leaves 22 or 28.
- Two left, and the bracket picks between them: 784 is nearer 900 than 400, so take the bigger one — 28.
- Check it: 28 × 28 = 784. So √784 = 28.
How it works.
- 01
√ asks a question: which number times itself gives 784? It does not mean half of 784.
- 02
Bracket it first. 20² = 400, which is under 784, and 30² = 900, which is over. So the answer is between 20 and 30.
- 03
Now the last digit. 784 ends in 4, and the only digits whose square ends in 4 are 2 and 8. Between 20 and 30 that leaves 22 or 28.
- 04
Two left, and the bracket picks between them: 784 is nearer 900 than 400, so take the bigger one — 28.
- 05
Check it: 28 × 28 = 784. So √784 = 28.