Advertisements
Advertisements
Question
The product of two irrational numbers is an irrational number (True/False).
Solution
The product of two irrational numbers is an irrational number (True/False)
False
Reason:
Let us assume the two irrational numbers be `sqrt2` and `sqrt3`
Sometimes, it is and sometimes it isn't.
`sqrt2` And `sqrt3` are both irrational as their product is `sqrt6`
Now `sqrt2` and `sqrt8` are both irrational but their product, `sqrt16 ` is rational (in fact, it equals 4)
APPEARS IN
RELATED QUESTIONS
Prove that the square of any positive integer is of the form 3m or, 3m + 1 but not of the form 3m +2.
Define HOE of two positive integers and find the HCF of the following pair of numbers:
32 and 54
Define HOE of two positive integers and find the HCF of the following pair of numbers:
75 and 243
Using prime factorization, find the HCF and LCM of 96, 404 In case verify that HCF × LCM = product of given numbers.
Using prime factorization, find the HCF and LCM of 12,15, 21 .
Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.
Express each of the following as a rational number in its simplest form:
(i`) 0.bar (8)`
When the positive integers a, b and c are divided by 13, the respective remainders are 9, 7 and 10. Show that a + b + c is divisible by 13
If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers are ______.
The LCM of two prime numbers p and q (p > q) is 221. Find the value of 3p - q.