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For this exercise, you need
♥ INTERNET EXPLORER 6.0 and above, with MathPlayer installed.♥
APPROXIMATING RADICALS
Jump right to the skill exercise
Jump right to the concept question exercise
The concepts for this exercise are summarized below.
For a complete discussion, read the text.
Here, you will practice with radicals that don't come out "nicely".
EXAMPLES:
Find the two closest integers between which the given radical lies.
Do not use the square root or cube root keys on a calculator.
7
lies between 2 and 3
Thought process:
We need a nonnegative number which, when squared, gives 7 .
22 = 4 ( 2 is too small)
32 = 9 ( 3 is too big)
293
lies between 3 and 4
Thought process:
We need a number which, when cubed, gives 29 .
33 = 27 ( 3 is too small)
43 = 64 ( 4 is too big)
-123
lies between -3 and -2
Thought process:
We need a number which, when cubed, gives -12 .
The answer will be negative.
Since it's easier to work with positive numbers, we first investigate
123 :
23 = 8 ( 2 is too small)
33 = 27 ( 3 is too big)
Thus, the cube root of 12 lies between 2 and 3 ,
and the cube root of -12 lies between -3 and -2 .
For this web exercise, you MUST must list the integers from least (farthest left) to greatest (farthest right).
EXAMPLE:
Estimate 130
to the nearest tenth.
(This is a non-calculator approach.)
Solution:
To round to the tenths place, we must know if the digit in the hundredths place is 5 or greater, or less than 5.
As above, first determine that 130
is between 11 and 12 .
Using long multiplication:
11.52
=132.25
so 11.5 is a bit too big
11.42
=129.96 so 11.4 is a bit too small
Thus,
130 lies
between 11.4 and 11.5 .
Again using long multiplication,
11.452
=131.1025 so 11.45 is a bit too big
Thus, the digit in the hundredths place must be less than 5 , and so the square root is closer to 11.4 .
Thus, 130≅11.4 .
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.