The number system is basically a representation of numbers in different forms and with different operators. The origin of the number system was a long time ago by our ancestors. Earlier they use the barter system until they don’t get introduced to Number System. They discover the method of counting. They might be used their fingers for counting and that’s maybe the reason that we have basic 10 digits i.e. 0 to 9.
SQUARE ROOT
A number multiplied by the same number produces a new number, then both multiplied numbers are known as the square root. The Square of a number can never be negative but the square root of a number can be negative and positive both. Every number have two square root except 0.
- Negative number have no square roots in natural number system.
- Square root of even number is even and square root of odd number is odd.
The positive square root is called the principle square root.
Square root is represented by the symbol ‘√’
CONCEPT: Prime Factorization Method
By using the concept of prime factorization we can get the square root of 196.
- Step-1: Find out all the prime factors of 196.
- Step-2: Arrange the same factors in pairs.
- Step-3: All the factors should be in pairs. If not then we can’t find the square root using the prime factorization method.
- Step-4: Multiply a number from each pair and that will be the principal square root and another square root will be the negative of the principal square root.
Example-: What are the two square roots of 196?
Solution:
First of all, find out the prime factor of 196.
196 = 2×2×7×7
We got two pair, First one is 2×2 and the other is 7×7.
Choose a number from each pair and multiply them.
= 2×7
= 14
So 14 is the first square root of 196 and the other square root will be negative of it i.e. -14.
√(196)=±14
Two square roots of 196 is +14 and -14.
Similar Questions
Question-1: What are the two square root of 225?
Solution:
Find out the prime factors of 225.
225 = 3×3×5×5
We got two pair of prime factor.
First one is 3×3 and second one is 5×5.
Choose a pair from each term and multiply them.
= 3×5
= 15
So, 15 is the first square root of 225 and another sqaure root is negative ot it i.e. -15.
√(225) = ±15
Two square roots of 225 is +15 and -15.
Question-2: If one square root of the number is 17 then find out the second square root of same number?
Solution: Every number has two square root, in form of ±.
If one number is positive then other will be negative but their absolute value will be same.
So, if one square root of a number is 17 then other will be -17.