Question

Which two numbers does the √12 fall between? √4 √9 √16 √25 To answer, type in the box below. To answer √4, you would type square root 4.

Answer 1

9 and 16...............................................

Answer 2

ANSWER


`√(9) \: and \: √(16)`

Step-by-step explanation

First, simplify the square roots.


`√(4) = \sqrt{ {2}^(2) } = 2`


`√(9) = \sqrt{ {3}^(2) } = 3`


`√(16) = \sqrt{ {4}^(2) } = 4`


`√(25) = \sqrt{ {5}^(2) } = 5`

Let us simplify t

`√(12)`
Although 12 is not a perfect square, it contains, a perfect square.


`√(12) = √(4 * 3) = √(4) * √(3) = 2 √(3)`

We can now observe that,


`3 \: < \: 2 √(3) \: < \: 4`

Therefore,


`√(9) \: < \: √(12) \: < \: √(16)`

Hence


`√(12)`
is between,


`√(9)`
and


`√(16)`