Ayush Agarwal Maths

Simple interest -  Simple interest  is  interest  calculated on the principal portion of a loan  to a savings account.

                   CUBES AND CUBE ROOTS Cube number- A cube number is a number multiplied by itself twice, or we can say the cube of a number m is its third power.  For example- m³ =  m  ×  m 2  =  m  ×  m  ×  m . 8³ = 8 × 8 2  = 8  × 8  × 8 = 512 .  15³ = 15  ×  15 2  =  15  ×  15  ×  15 = 3375 .   Perfect cube - A natural number is said to be a perfect cube if it is the cube of some natural numbers.  Examples-   1 ³ = 1, 2³ = 8, 3³ = 27, 4³ = 64,  etc.            Thus 1, 8, 27, 64 etc.., are perfect cubes.  Facts About cube numbers:- 1. The cube of a number is that number raised to the power 3 .  2. The cube of an even natural number is even.  3. The cube of an odd natural number is odd.  4.  Numbers ending in 1, 2, 3, 4, 6, 7...

          SQUARES AND SQUARE ROOTS   Square number - The square of a number is the product of the number with the number itself.  A given number is a perfect square if its prime factors can be expressed in pairs of equal factors.  A perfect square number is never negative. For example - 8^2 = (8×8) = 64 Facts About Squares -  1. A number ending in 2, 3, 7 or 8 is never a perfect square.  2. A number ending in an odd number of zeros is never a perfect square.  3. The square of an even number is always even.  4. The square of an odd number is always odd.  5. The ending digits of a square number is 0, 1, 4, 5, 6, or 9 only.  Note:- It is not necessary that all numbers ending with digits 0, 1, 4, 5, 6, or 9 are square numbers.  Important Facts-  1. Numbers ending in an even number of zeros are not necessarily perfect squares. Eg- 3700, 290000, 47000000.   Practice Questio...