Between which two successive intergers do the following irrational numbers lie?
A.√167
B.^3√80
which irrational numbera lies between 5and6?
what, no calculator? Evaluate the radicals and you will get a decimal number. For example,
√412 = 20.297
so, it lies between 20 and 21
As for the 2nd part, consider any irrational number less than 1, say, √.73 = .854
So, 5 < 5+√.73 < 6
ot, consider that
5^2 = 25
6^2 = 36
So,
5 < √28 < 6
5 < √34 < 6
and so on
To find between which two successive integers the given irrational numbers lie, we can simply calculate the integer values that are smaller and larger than each irrational number.
A. √167:
To determine the integers between which √167 lies, we need to calculate the square roots of the closest perfect squares. In this case, the closest perfect squares to 167 are 144 (12*12) and 169 (13*13). Now we can conclude that √167 lies between √144 and √169. Simplifying, we have √167 ≈ 12.96. Therefore, it lies between the integers 12 and 13.
B. ^3√80:
For ^3√80, we need to find the two perfect cubes between which it falls. The closest perfect cubes smaller than 80 are 64 (4^3) and 125 (5^3). Thus, we can conclude that ^3√80 lies between ^3√64 and ^3√125. Simplifying these, we get ^3√80 ≈ 4.309. Therefore, it lies between the integers 4 and 5.
Regarding the second part of your question, you have asked which irrational number lies between 5 and 6. Assuming you are referring to the square root of a number, we can calculate the square roots of 25 and 36 to check which irrational number is between them.
The square root of 25 is 5, and the square root of 36 is 6. Therefore, there is no irrational number between 5 and 6 in terms of square roots.
However, if you have asked about a different type of irrational number, please provide more details so I can give you a more accurate answer.