compare the surds (9,3✓2
Answers
Answer:
In case of comparison between two or more non-equiradical surds (i.e., surds of different orders) we express them to surds of the same order (i.e., equiradical surds). Thus, to compare between ∛7 and ∜5 we express them to surds of the same order as follows:
Clearly, the orders of the given surds are 3 and 4 respectively and LCM Of 3 and 4 is 12.
Therefore, ∛7 = 71/3 = 74/12/ = 74−−√12 = 2401−−−−√12 and
∜5 = 51/4 = 53/12 = 53−−√12 = 125−−−√12
Clearly, we see that 2401 > 125
Therefore, ∛7 > ∜5.
If the surds are not in same order or non-equiradical, then we need to express the surds in the order of Lowest Common Multiple (LCM) of other surds. By this way, all the surds can be written in same order and we can compare their values by comparing the values of radicand.
For example we need to compare the following surds and arrange them in a descending order.
3–√2, 5–√3,12−−√4.
The surds are in the order of 2, 3, and 4 respectively. If we need to compare their values, we need to express them in same order. As the LCM of 2, 3, and 4 is 12, we should express the surds in order 12. We know surds can be expressed in any order in multiple of their lowest order.
3–√2 = 312 = 3612= 729112 = 729−−−√12
5–√3 = 513 = 5412= 625112 = 625−−−√12
12−−√4 = 1214 = 12312 = 1728112 = 1728−−−−√12
Now all three surds are expressed in same order. As 1728 > 729 > 625
the descending order of the surds will be 12−−√4, 3–√2, 5–√3.