The value obtained after calculating the square root will be the length of its side. For instance, 42 = 16, square root of 16 is 4 and so on. 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(iii) Combine the like square root terms using mathematical operations. For finding the square root, firstly we have to pair the common factors. This can easily be done by finding the square root of the area. Performance & security by Cloudflare, Please complete the security check to access. In the same way, the inverse of squaring a number is finding its root. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Step IV: Take one factor from each pair. (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 Required fields are marked *, \(\underline{2~ ×~ 2} ~×~\underline{ 2 ~×~ 2} ~×~ \underline{2~ ×~ 2} ~×~\underline{ 3~ ×~ 3}\). Step VI: The product obtained in step V is the required square root. (ii) Make the pair of similar factors such that the both factors in each pair are equal. (i) 2304 Thus, Square root of 2304 = 48Let’s look at individual steps as well Individual Steps are explainedStep 1:Write the numberWe make pairs from right.So, 04 and 23 are two pairs. (iii) Take one factor from pair. For example, the area of a square is 225. This article covers the method of prime factorisation. Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. 1 | 1 ∴ Prime Factorization of 7921 = 89 × 89 ∴ √7921 = √(89 × 89 = 89 Hence, the square root of 7921 is 89 Another way to prevent getting this page in the future is to use Privacy Pass. For example, the square root of 9 is √9 = √(3×3) = 3. Now, what if the area of the square is given, and we have to calculate the length of its side? Your IP: 87.106.42.115 The inverse process of subtraction is addition and of division is multiplication. We can see, 9 is a perfect square and hence it is easier to find the root of such numbers. For example, let us find the prime factors of 576. Ex 6.4, 1 Find the square root of each of the following numbers by Division method. Step V: Find the product of factors obtained in step IV. Finding square root by prime factorisation is an easy method. Let us see here some more examples to find square root of numbers. Also, take free tests to practice for exams. Your email address will not be published. To learn more about other topics download BYJU’S – The Learning App and watch interactive videos. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. Square root of a number is the value that returns the original number on multiplied by itself. Square root through prime factorisation - law To find the square root of the given number through prime factorization method we follows the following steps: (i) First we divide the given number in to its prime factor. It can be observed that the prime factors in the prime factorisation of a square number, occur twice the number of times, it occurs in the number itself. (ii) Inside the square root, for every two same numbers multiplied, one number can be taken out of the square root. For example, the square root of 9 is √9 = √(3×3) = 3. 89 | 89. We need to factories the number under the root and pair them in two. • If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. In a square, all the sides have the same length. Your email address will not be published. For imperfect squares, we can use long division method to find the square root. The orange divisor(s) above are the prime factors of the number 768. We need to factories the number under the root and pair them in two. Its length will be: Therefore, the side of the square is 15 units. (i) Decompose the number inside the square root into prime factors. Let us consider the prime factors of a number and its square. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors. • Area of a square is the product of its sides. \(576\) = \(\underline{2~ ×~ 2} ~×~\underline{ 2 ~×~ 2} ~×~ \underline{2~ ×~ 2} ~×~\underline{ 3~ ×~ 3}\), \(\Rightarrow~ 576\) = \(2^2~ × ~2^2 ~× ~2^2~ ×~ 3^2\). Hence, if one of the sides is known then the area can be easily calculated. Area of square = Side × Side = Side2. Another way to do prime factorization is to use a factor tree. For example 12 and 144. You may need to download version 2.0 now from the Chrome Web Store. Solution - 89 | 7921. Cloudflare Ray ID: 5f99618cdcbb1f19 Thew following steps will be useful to find square root of a number by prime factorization. Below is a … If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 768. 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