Video Transcript
Which of the following statements
is true? All five of the statements want us
to evaluate the square root of 17. Option (A) says, the answer is
between three and 3.5. Option (B) the answer is between
3.5 and four. Option (C) the answer is between
four and 4.5. Option (D) the answer is between
4.5 and five. Or option (E) the answer is between
five and 5.5.
We will begin this question by
drawing a number line to establish which two integer values the square root of 17
lies between. Let’s consider the integer values
from three to six. We know that square rooting a
number is the opposite of squaring it. As three squared is equal to nine,
the square root of nine is equal to three. This means that we can put the
radicals, the square root of nine, square root of 16, square root of 25, and square
root of 36, on our number line.
The number 17 lies between 16 and
25. Therefore, the square root of 17 is
greater than the square root of 16 and less than the square root of 25. We know that the square root of 16
is equal to four and the square root of 25 is equal to five. We can, therefore, conclude that
the radical, square root of 17, lies between four and five. We can, therefore, eliminate
options (A), (B), and (E).
4.5 is halfway between four and
five. 17 is much closer to 16 than
25. It is one away from 16 but eight
away from 25. This means that the square root of
17 will be closer to the square root of 16 than the square root of 25. We can, therefore, conclude that
the square root of 17 lies between four and 4.5. This means that statement (C) is
true. If you evaluate the square root of
17, the answer is between four and 4.5.
