cube root of 64 by prime factorization

cube root of 64 by prime factorization The following steps can be applied to determine the cube root of any number using the prime factorization method In this case this method is applied to find sqrt 3 64 Step 1 Find the prime factors of the given number that is 64 So the prime factorization of 64 is 64 2 x 2 x 2 x 2 x 2 x 2

Cube Root of 64 by Prime Factorization Step 1 Determine the prime factorization of 64 i e 64 2 2 2 2 2 2 Step 2 Group the prime factors of 64 in groups of three each 64 2 2 2 2 2 2 2 3 2 3 Step 3 Use the law of exponents 64 2 3 2 3 4 3 Step 4 Take the cube root on both sides of the equation The prime factorization of 64 can be calculated as 2 64 2 32 2 16 2 8 2 4 2 2 1 So 64 2 2 2 2 2 2 Then the cube root of 64 is 64 3 2 2 2 2 2 2 3 64 3 2 2 2 2 2 2 3 64 3 2 2 64 3 4 Hence the cube root of 64 is 4 Suggest Corrections 14 Similar questions Q Question 1 i

cube root of 64 by prime factorization

cube root of 64 by prime factorization
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This is a step by step video tutorial on How to Find Cube Root of 64 by Prime Factorization 64 cube root by prime factorization Factors of 64 64 ka cube root Show more Solution 4 is the cube root of 64 Or we can write as 64 4 Example 3 Find the cube root of 729 Solution Steps are as follows Step 1 Take the given number The number is 729 Step 2 Find the prime factors of given number prime factors of 729 9 x 9 x 9 Step 3 Grouping numbers in such a way that one group of three same prime

Step 1 By prime factorisation of 64 we get 64 2 2 2 2 2 2 Step 2 Pair the factors of 64 in a group of three such that they form cubes 64 2 2 2 2 2 2 64 2 3 2 3 Using the law of exponent we get 64 2 3 3 2 6 a m a n a m n Or 64 2 2 3 a m n a mn 64 4 3 64 2 2 2 2 2 2 64 2 2 2 2 2 2 Since 2 occurs in triplets 64 is a perfect cube So the cube root of 64 is 2 2 4 2 2 4 Note An alternative method can be by simply finding the factors by breaking the number into smaller numbers and then taking the cube root

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So 64 3 64 3 4 The cube root of a number x is denoted as x 3 x 3 or x The cube of natural numbers is called the perfect cube numbers Any perfect cube number will have a cube root equal to a whole number Cube root of a number can be found either by estimation method or by prime factorization method Factorization Method to Find the Cube Root We can easily find the cube root of a given number by using the method of factorization To determine the cube root of a given number proceed as given below Step I write the given number as the product of primes Step II Create a group in triplets of the same prime Step III

In order to simplify cube root of 64 by using prime factorization method you follow these steps Find prime factors of 64 Group the factors in 3 in such a way that each number of the group is same Take one factor from each group Find the product of the factors obtained in step 3 This product is the required cube root Here is the factor tree for 64 So the prime factorization of 64 is 2 2 2 2 2 2 We re looking for A 64 3 so we want to split the prime factors into three identical groups Notice that we can rearrange the factors like so 64 2 2 2 2 2 2 2 2 2 2 2 2 So 2 2 3 4 3 64 So A 64 3 is 4 Practice

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cube root of 64 by prime factorization - 64 2 2 2 2 2 2 64 2 2 2 2 2 2 Since 2 occurs in triplets 64 is a perfect cube So the cube root of 64 is 2 2 4 2 2 4 Note An alternative method can be by simply finding the factors by breaking the number into smaller numbers and then taking the cube root