## Prove that the difference and quotient of 3+2√3 and 3-2√3 are irrational

Prove that the difference and quotient of 3+2√3 and 3-2√3 are irrational Solution:

## show that (n²-1) is divisible by 8, if n is odd positive integer.

show that (n²-1) is divisible by 8, if n is odd positive integer. Solution:

## x and y are odd positive integers then x²+y² is even but not divisible by 4

Prove that if x and y are odd positive integers then x²+y² is even but not divisible by 4 Solution:

## Show that one and only one out of n, (n+2) or (n+4) is divisible by 3, where n∈Ν

Show that one and only one out of n, (n+2) or (n+4) is divisible by 3, where n∈Ν Solution :

## Use Euclid’s division algorithm to find the HCF of 4052 and 12576

Use Euclid’s division algorithm to find the HCF of 4052 and 12576 12576 = 4052 × 3+ 420 4052= 420 ×9 272 420= 272 ×1 + 148 272= 148 × 1 +124 148= 124 × 1+ 24 124 =24  ×5 Read More …

## HCF of two numbers is 23 and their LCM is 1449.

Given that HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other. Solution : HCF × LCM = a × b 23 × 1449 = 161 × b b = (23 × 1449 )/161 Read More …

## Find the greatest of 6 digits exactly divisible by 24, 15 and 36

Find the greatest of 6 digits exactly divisible by 24, 15 and 36 The greater number of 6 digits is 999999. LCM of 24, 15, and 36 is 360. 999999 = 360 ×2777  +279 Re quired No. is 999999 -279 Read More …

## finding HCF

144 cartoons of coke can and 90 cartoons if Pepsi can are to be stacked in a canteen It each stack is of the same height and is to contain cartoons of the same Drink. What would be the greater Read More …

## Prove that Product of three consecutive positive integers is divisible by 6.

Prove that Product of three consecutive positive integers is divisible by 6. solution:

## positive even integer is of the from 2q

Show that every positive even integer is of the from 2q and that every positive odd integer is the four 2q+1 for some integer q. Solution: Let a=bq+r : b=2 0 ≤ r<2 i.e. r=0, 1 a=2q+0, 2q+1, If a=2q Read More …