We know that the irrational number is between:
6 < √45 < 7
And a good estimation is √45 = 6.71
How to approximate the irrational number?
Here we just need to find a lower and upper bound for the given irrational number.
To do it, we just need to find a square number larger and a square number smaller than the number inside the square root.
The larger one will be:
7*7 = 49
The smaller one will be:
6*6 = 36
Then we can write:
√36 < √45 < √49
6 < √45 < 7
So we now know that our number is between 6 and 7, that is already a good estimation, now you can also try to see if it is closer to 6 or 7, by taking the direct square root you will get:
Now just take the product between numbers of the form:
6.10*6.10 = 37.21
And so on, until we almost reach 45.
We will get:
6.71*6.71 = 45.02
So a good estimation is √45 = 6.71
If you want to learn more about irrational numbers:
https://brainly.com/question/20400557
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