Step II: Make pairs of similar factors. So, the square root of 3 lies between 1 and 2. Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. (ii) Make the pair of similar factors such that the both factors in each pair are equal. Square root of a number is represented as the number written within the symbol ‘√’. The identical prime factors are paired and the product of one element from each pair gives the square root of the number. Example: Evaluate the square root of 3 using the average method. Square root is one of the most important functions in Mathematics which has a wide range of applications in day to day life and also scientific calculations. Square root is one of the most important functions in Mathematics which has a wide range of applications in day to day life and also scientific calculations. Square root of an even square number is even and that of an odd square number is odd. (i) 729We use prime factorization to find square root.Thus, 729 = 3 × 3 × 3 × 3 × 3 × 3Square root of 729 = 3 × 3 × 3 = 9 × 3 = 27 Ex 6.3, 4 Find the square roots of t Numbers ending with an odd number of zeros do not square roots. For example, the square root of 9 is √9 = √(3×3) = 3. To find the square root of a perfect square by using the prime factorization method when a given number is a perfect square: Step I: Resolve the given number into prime factors. A number's factors are any set of other numbers that multiply together to make it. Numbers ending with an even number of zeros have half the number of zeros in their square root. There are several methods to find the square root of a number among which a few familiar ones are: Finding Square Root Formula by Prime Factorization Method. Example: If ‘x’ = 7, find the square root of x by guess and check method. Divide your number into perfect square factors. What is Root in Mathematics of Perfect Square Number Properties? This is a method in which the number whose square root is to be determined is repeatedly subtracted by the consecutive odd number till the difference becomes zero. Square root of a number ‘x’ can be written in exponential form as (x)1/2. Square roots of negative numbers are imaginary. Square root of any number in Mathematics is that number which when multiplied by itself gives the product equal to the number whose square root is to be determined. Evaluate the square root of 3 using the average method. It is very important to understand what is a square root of a perfect square number before making yourself clear about what is a root in math. Pro Lite, Vedantu (iii) Take one factor from pair. In this method, the concept of average is used to find the square root of a given decimal number. So, the square root of 16 is 4. i.e. The number of subtractions give the root of the number.This method can only be used to find the square root of perfect square numbers. 1. NCERT Solutions for Class 9 Maths Chapter 12 Heron's Formula, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots, NCERT Solutions for Class 9 Maths Chapter 12 Heron's Formula In Hindi, NCERT Solutions for Class 9 Maths Chapter 12 Heron's Formula (Ex 12.2) Exercise 12.2, NCERT Solutions for Class 8 Maths Chapter 6- Squares and Square Roots Exercise 6.4, NCERT Solutions for Class 9 Maths Chapter 12 - Heron s Formula Exercise 12.1, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots in Hindi, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.1) Exercise 6.1, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.3) Exercise 6.3, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.2) Exercise 6.2, CBSE Class 8 Maths Chapter 6 - Squares and Square Roots Formulas, Vedantu

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