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Here’s an unshmoopy question you’ll find on the exam…
The number “square root of 35” is between which of the following numbers?
And here are the potential answers:
Before we spoil the ending and kill all the drama… why not hit pause and try to solve
it yourself first? So what’s this question asking? Well, really
just whether we have a clue as to the relative size or scale of squares and roots.
Easy to brute force this one.
Look at the potential answers.
Try squaring 3 – it’s 9.
Square 4 – its 16… so, nope.
The square root of 16 is smaller than the square root of 35. Move on. Try B.
We know we need a much bigger 2nd number… so square 5.
It’s still not bigger than 35…5 squared is just 25.
Try the 6 in C – it’s 36 – voila. Answer C. Done.
Of course, this problem could get much more complicated if we were using… extensions.