Define a perfect number. Write two perfect numbers.

STATEMENT-1 : The dual statement of "xis a perfect square or xis a prime number" is "x is a perfect square and a prime number and STATEMENT-2 : If x is a prime number, then it isnot a perfect square.

using the method of successive subtraction examine whether or not the following numbers are perfect cube (i) 130 (ii) 345 (iii) 792 (iv) 1331 Find the smallest number that must be subtracted from those of the numbers in above question which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?

A number is selected from first 100 natural numbers. The probability that number is perfect square or a perfect cube is

Prove that sqrt(n) is not a rational number. if n is not a perfect square.

Prove that sqrt(n) is not a rational number. if n is not a perfect square.

Show that \ 1331 is a perfect cube. What is the number whose cube is \ 1331 ?

Write the converse of the following statement (i) If a number n is odd , then n^2 is odd If a number is divisble by 6 , then it is divisble by both 2 and 3 (iii) If root3a is an irrational number then a is not a perfect cube

For each of the following, find the least number that must be added so that the resulting number is a perfect square. (i) 511 (ii) 7172 (iii) 55078

For each of the following, find the least number that must be subtracted so that the resulting number is a perfect square. (i) 796 (ii) 1886 (iii) 23497

Let A be the least number such that 10A is a perfect square and 35 A is perfect cube. Then the number of positive divisors of A is :