Approximating square roots Go to le
Without using a calculator, choose the statement that best describes the value of 215.
Choose 1
The value of 215 is between 13 and 13.5.
The value of 215 is between 13.5 and 14.
The value of 215 is between 14 and 1.5.
The value of v 215 is between 14.5 and 15.

Step-by-step explanation:

We know that

14^2=196, and

15^2=225

so we know that sqrt(215) is between 14 and 15.

How do we know if it is between 14.5 and 15?

we need to know the value of 14.5^2, which we can calculate in the head as follows:

The square of all numbers ending in 5 such as 15 can be calculated by breaking up the 5 and the preceding digit(s),

The preceding digit is 1.  We multiply 1 by the next integer, 2 to get 2.

Attach 25 to 2 gives us 225 (as we saw above.

Example, 145*145 = 14*15 | 25 = 210 | 25 = 21025

so

14.5^2 = 210.25, which gives the more precise answer that

14.5^2 < 215 < 15^2, or

14.5 < sqrt(215) < 15  (fourth choice)

Since the third choice says sqrt(215) is between 14 and 1.5 (not 15), so the third choice is incorrect.

Note: if we eliminated the third choice, i.e. discard the likelihood of typo in the question, the only one left is the fourth choice.

step-by-step explanation:

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