Question

Which of the following pairs of numbers provide the best estimate of start root 53 end root?

start root 36 end root and start root 64 end root

start root 64 end root and start root 81 end root

start root 36 end root and start root 49 end root

start root 49 end root and start root 64 end root

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To estimate the square root of 53, we should look for the perfect squares that are closest to 53.

Here are the perfect squares mentioned in the options:

√36 = 6
√49 = 7
√64 = 8
√81 = 9

Now, we need to find which two perfect squares are closest to 53 and "sandwich" it between them:

- 36 < 53 < 49 is not correct because 53 is not between 36 and 49.
- 64 < 53 < 81 is not correct because 53 is not between 64 and 81.
- 36 < 53 < 49 is again mentioned incorrectly.
- 49 < 53 < 64 is correct because 53 is between 49 and 64.

So, the accurate approximation for the square root of 53 would lie between the square roots of 49 and 64. This means that the best estimate would be between √49 and √64, which are 7 and 8, respectively. Therefore, the last option is correct:

√49 and √64