Advertisements
Advertisements
प्रश्न
Prove that following numbers are irrationals:
उत्तर
(i) Let us assume that `2/sqrt7` is rational .Then , there exist positive co primes a and b such that
`2/sqrt7=a/b`
`sqrt7=(2b)/a`
`sqrt7`is rational number which is a contradication.
Hence `2/sqrt7` is irrational
APPEARS IN
संबंधित प्रश्न
Define HOE of two positive integers and find the HCF of the following pair of numbers:
75 and 243
Find the largest number which divides 320 and 457 leaving remainders 5 and 7 respectively.
Express each of the following as a rational number in its simplest form:
(i`) 0.bar (8)`
Express 360 as product of its prime factors
Express each of the following integers as a product of its prime factors:
7325
Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Every odd integer is of the form 2m − 1, where m is an integer (True/False).
The product of two irrational numbers is an irrational number (True/False).
The sum of the exponents of the prime factors in the prime factorisation of 196, is
The LCM and HCF of two rational numbers are equal, then the numbers must be