Question

Find √10 to the nearest hundredth.Explain how you found your answer.

Answer 1

the square root of 10 is 3.16 because 3.16 times 3.16 equals 10

Answer 2

Answer: 3.16

Explanation:

We do know (without calculator) the square root of 9 and of 16

`√(9) = 3`

`√(16) = 4`

And we know that
`9 < 10 < 16`

So,
`√(9) <√(10) <√(16)`

`3 < √(10) < 4`

So
`√(10)` is in the middle of 3 and 4, and because 10 is closer to 9 than to 16, the
`√(10)` is closer to 3.

Now,

We divide
`(10)/(3) = 3.33`

And we average 3 and 3.33:
`(3+3.33)/(2) = 3.17`

Again,
`(10)/(3.17) = 3.16`

And if we make with calculator
`√(10) = 3.162278`

So the value that we find is good
`√(10) = 3.16`