How do you know whether #sqrt38# is is closer to 6 or 7 without using a calculator?

Answer 1

Closer to 6

It is true that we can look at this and think the answer is closer to 6 but can we prove it?? Look at the half way point 6.5 6.5x 6.5 (6x 6.5 ==39, 0.5x 6.5= 3.25) #6.5^2=42.25#
38<42.25 so #sqrt38#. < halfway between 6 and 7
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Answer 2

Without using a calculator, you can approximate the square roots by finding perfect squares that are closest to (38). Since (38) is between (36) ((6^2)) and (49) ((7^2)), you can compare (38) to the midpoint of these two perfect squares, which is (42.5). Since (38) is closer to (36) than (49), (\sqrt{38}) is closer to (6) than (7).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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