between which two successive interger do the following irrational numbers lie?
A.√167
B.^3√80
let's see:
12^2 = 144
13^2 = 169
14^2 = 196
what do you think?
if ^3√80 is to mean "the cuberoot of 80"
then we could try this as well:
2^3 = 8
3^3 = 27
4^3 = 64
....
Which irrational number lies between 5 and 6
To determine between which two successive integers the given irrational numbers lie, we can use estimation.
A. √167:
Step 1: Find the square root of the closest perfect square to 167.
The perfect square immediately below 167 is 144 (12 x 12), and its square root is 12.
Step 2: Find the square root of the next perfect square.
The perfect square immediately above 167 is 169 (13 x 13), and its square root is 13.
Therefore, the square root of 167 (√167) lies between 12 and 13. So, the answer for √167 is between the integers 12 and 13.
B. ^3√80:
Step 1: Find the cube root of the closest perfect cube to 80.
The perfect cube immediately below 80 is 64 (4 x 4 x 4), and its cube root is 4.
Step 2: Find the cube root of the next perfect cube.
The perfect cube immediately above 80 is 125 (5 x 5 x 5), and its cube root is 5.
Therefore, the cube root of 80 (^3√80) lies between 4 and 5. So, the answer for ^3√80 is between the integers 4 and 5.
In conclusion:
A. The number √167 lies between the integers 12 and 13.
B. The number ^3√80 lies between the integers 4 and 5.