how many odd natural numbers must be subtracted from the perfect square 81 to find its square root
Answers
If a natural number m can be expressed as n2 , where n is also a natural number, then m is a square number.
Properties of square numbers are explained in this chapter.
If a number has 1 or 9 in its units place, then its square ends in 1.
When a square number ends in 6, then its square root will have 4 or 6 in its unit's place.
Square numbers can only have even number of zeroes at the end.
Some interesting patterns discussed in this chapter are:
a. Adding triangular numbers
b. Numbers between squares: There are 2n non-perfect square numbers between the squares of the numbers n and (n + 1)
c. Adding odd numbers: If a natural number cannot be expressed as a sum of successive odd natural numbers starting with 1, then it is not a perfect square.
d. A sum of consecutive natural numbers
e. Product of two consecutive even or odd natural numbers
f. Some more pattern in square numbers
Section 6.4 deals with the topic- Finding the square of a number. This involves finding the square of a number without actual multiplication. This section is subdivided into the following points:
1. Other patterns in squares
2. Pythagorean triplets
The collection of numbers 3, 4 and 5 is known as the Pythagorean triplet.
Another section 6.5 gives details about square roots. Square root is the inverse operation of a square.
Different methods of finding square roots are discussed. The section further subdivides into the following sections:
1. Finding square roots
2. Finding square root through repeated subtraction
3. Finding square root through prime factorisation.
4. Finding square root by division method
This is followed by finding the Square Roots of Decimal, the topic is explained in 6 steps. Students need to go through these steps thoroughly to understand the concept clearly. After that, the concept of Estimating Square Roots is also explained.