Question

Help me algebra please

Answer 1

We'll need the list of perfect squares. The first few are:

1, 4, 9, 16, 25, 36, 49, 64, ...

We stop here because 64 is larger than 55

Based on that list, 49 < 55 < 64

We then take the square root of each piece to have these steps

`49 < 55 < 64\\\\√(49) < √(55) < √(64)\\\\7 < √(55) < 8`

This proves that
`√(55)` is between integers 7 and 8.

A calculator further can verify this because
`√(55) \approx 7.416`

Now let's find the gap between 55 and each perfect square endpoint

55 - 49 = 6

64 - 55 = 9

The smaller gap size is 6. It shows that 55 is closer to 49, compared to 64.

Therefore
`√(55)` is closer to 7 compared to 8

This is confirmed when looking at the approximation
`√(55) \approx 7.416`