Square and Square roots : NCERT / CBSE Revision notes
We know that a number m is called a square number if it is expressed as n2. Here n is called the square root of m. Square root is the inverse operation of squares. Every square number is a sum of the first n odd natural numbers.
A set of three numbers that satisfies the Pythagoras Theorem is called Pythagorean Triplet. Pythagorean Triplets can be found using a general expression (2m)2 + (m2 – 1)2 = (m2 + 1)2, where m is any natural number greater than one.
Square root of a given number is a number whose square is equal to the given number. Positive square root of a number is denoted by the symbol √.
Square root of a number can be found using the following three methods:
- Repeated Subtraction Method
- Prime Factorisation Method
- Long Division Method
Repeated subtraction method
We can find the square root of a given number using Repeated subtraction method:
- Subtract successive odd numbers from the given number starting from 1 till the difference becomes zero.
- Count the number of steps it took to get the difference as zero.
Prime factorization method
To find the square root by prime factorization method:
- Find the prime factors of the given number.
- Form pairs of prime factors.
- Take one prime factor from each pair of prime factors of the given number.
- Find the product of these prime factors to get the square root of the given number.
If prime factors of a number do not occur in pairs, the given number is not a perfect square.
Long Division Method
1.Draw lines over pairs of digits from right to left.
2.Find the greatest number whose square is less than or equal to the digits in first group.
3.Take this number as the divisor and quotient of the first group and find the the remainder.
4.Move the digits from the second group besides the remainder to get the new dividend.
5.Double the first divisor and bring it down as the new divisor.
6.Complete the divisor and continue the division.
7.Repeat the process till the remainder becomes zero.
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