Question

What two integers does sqrt41 fall between? explain reasoning

Answer 1

Below!

Explanation:

Given square root:

`\sqrt41`

Let's note a few perfect square roots.

`1 = √(1 * 1) = √(1)`

`2 = √(2 * 2) = √(4)`

`3 = √(3 * 3) =√(9)`

`4 = √(4 * 4) =√(16)`

`5 = √(5 * 5) =√(25)`

`6 = √(6 * 6) =√(36)`

`7 = √(7 * 7) =√(49)`

`8 = √(8 * 8) =√(64)`

And so on...

When looking at the perfect square roots we identified, we can say that:

`√(36) < √(41) < √(49)`

Therefore,

`6 < √(41) < 7`

We can conclude that
`√(41)` is between 6 and 7.

Answer 2

Let's check the squares of first 10 number

• 1²=1
• 2²=4
• 3²=9
• 4²=16
• 5²=25
• 6²=36
• 7²=49
• 8²=64
• 9²=81
• 10²=100

41 lies between 36 and 49

Hence

• √41 lies in between 6 and 7