Advertisements
Advertisements
Question
Prove that \[2\sqrt{3} - 1\] is an irrational number.
Solution
Let us assume that \[2\sqrt{3} - 1\] is rational .Then, there exist positive co primes a and b such that
`2sqrt3-1=a/b`
`2sqrt3=a/b+1`
`sqrt 3=(a/b+1)/2`
`sqrt3=(a+b)/(2b)`
This contradicts the fact that `sqrt3` is an irrational
Hence `2sqrt3-1` is irrational
APPEARS IN
RELATED QUESTIONS
Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively.
During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both and the same number of pencils and crayons, how many of each would you need to buy?
Find the smallest number which when divides 28 and 32, leaving remainders 8 and 12 respectively.
Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
(i) `17 /320`
Without actual division show that each of the following rational numbers is a non-terminating repeating decimal.
(i)`64/455`
If a and b are two prime numbers then find the HCF(a, b)
Show that \[3 + \sqrt{2}\] is an irrational number.
The product of any three consecutive natural number is divisible by 6 (True/False).
If a and b are relatively prime numbers, then what is their HCF?
