Advertisements
Advertisements
Question
Prove that \[4 - 5\sqrt{2}\] is an irrational number.
Solution
Let us assume that \[4 - 5\sqrt{2}\] is rational .Then, there exist positive co primes a and b such that
`4-5sqrt2=a/b`
`5sqrt2=a/b-4`
`sqrt2=(a/b-4)/5`
`sqrt5=(a-4b)/5b`
This contradicts the fact that `sqrt2`is an irrational
Hence `4-5sqrt2` is irrational
APPEARS IN
RELATED QUESTIONS
Using Euclid's division algorithm, find the H.C.F. of (iii) 867 and 255
Express the HCF of 468 and 222 as 468x + 222y where x, y are integers in two different ways.
Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
(i) `23/(2^3 × 5^2)`
Without actual division show that each of the following rational numbers is a non-terminating repeating decimal.
(i)`64/455`
The remainder when the square of any prime number greater than 3 is divided by 6, is
Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy
HCF of 8, 9, 25 is ______.
Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.
