Chap 6 SQUARES AND SQUARE ROOTS

Chap 6

SQUARES AND SQUARE ROOTS

SOME IMPORTANT FACTS

1.      The Square of a number Is that number raised to the power 2.

2.      A natural number n is a perfect  square , if n= m² for some natural number m.

3.      The cube of even natural number is even.

4.      The cube of odd natural number is odd.

5.      A number ending in 2, 3, 7, 8, is never a perfect square .

6.      A number ending in an odd number of zeros is never a perfect square.

7.      For any natural number n , we have ;  n² = Sum of first n odd natural numbers.

8.      There are 2n  non perfect sqare numbers between the squares of the numbers n and      ( n + 1 ).

9.      Formula for finding the number of digits in the square root of a perfect square :

Let there be a perfect square number containing  n digit. Then , its square root will contain ( n / 2 ) digits, when n is even, and ( n + 1/ 2 ) digits  when n is odd.

10.  For any natural number m > 1 , ( 2m, m2 -1 and m2+1 ) is Pythagoras triplet.

11.  The square root of a number x is that number which when multiplied by itself gives x as the product and the square root of x  is denoted by √x

12.                        For finding the square  root of a perfect  square, resolve it into prime factors, make pairs of similar factors and take the product of prime factors, choosing one out of every pair.

13.  For finding the square root of a decimal fraction, make even numbers of decimal places by affixing a zero, if necessary; mark off periods and extract the square root, putting the decimal point in the square root as soon as the integral part is exhausted .