# cube root of 64 by prime factorization method

Cube Root of 64. 216 = … After that, we will pair the factors in a group of three to represent them as cubes. Ex 7.2, 1 Find the cube root of each of the following numbers by prime factorisation method. Solution: [Image will be Uploaded Soon] 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 $\sqrt[3]{46656}$ = 2 x 2 x 3 x 3 = 36. 4 Answers. As an example the cube root of 64 is 4 and it is mathematically expressed as 4³ = 4 ×4 × 4 = 64 or 7³ = 7 × 7 × 7 = 343. both 2 × 2 = 4 and 2 + 2 = 4 and hence 22 = 4. The Prime factors of number 64 are 2 which in the form of equation is expressed as: 2× 2 × 2× 2 × 2 × 2. Number 9 is not divisible by 2 evenly, so we will skip it. You might be wondering how and why this is so. Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. Number 8 has four factors 1, 2, 4, and 8 itself. Prime Numbers Less Than 64 Are as Follows, Prime Numbers Greater Than 64 Are as Follows. (v) 15625We see that Ex 7.2, 1 Find the cube root of each of the following numbers by prime factorisation method. Since 2, 5 & 3 occur in triplets He has been teaching from the past 9 years. Step IV. Find the Cube Root of 46656 Using the Prime Factorization Method. And amazingly, even the smallest common factor, as well as the most significant common factor of 64, is number 2. Terms of Service. Last updated at Sept. 11, 2018 by Teachoo, Subscribe to our Youtube Channel - https://you.tube/teachoo, Ex 7.2, 1 Find the cube root of each of the following numbers by prime factorisation method. Cube Root of 216. ∴ 27000 is a perfect cube. How do I find the cube root of 74088 by prime factorisation method? = 25. The uniqueness of the number 4 is that the result of its multiplication and addition with its factor 2 gives the same result i.e. Number 4 is linear, which is also the 1st composite number and, therefore, the 1st non-prime number after the number one. Since, 216 is perfect cube of 6, hence we can find the cube root of 216 by factorisation. Cube root of 64 = 2 × 2= 4Ex 7.2, 1 Find the cube root of each of the following numbers by prime factorisation method. Example 2: Evaluate the Cube Root of 9261. 27000 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5 Keep going on until you arrive at 5 (9 / 2, rounded up). That said, the cube root of a number y is that number whose cube results in y. Note the numbers 4 and 5 so you know where to stop later. (iv) 27000We see that Read More. Since 2 & 11 occur in triplets Learn Science with Notes and NCERT Solutions. ∴ 10648 is a perfect cube. Let’s Quickly Find the Cube Root Using Step by Step Procedure With an Explanation, Using the method of prime factorization, we have, non-prime number after the number one. Factorization Method to Find the Cube Root. The Process of Prime factorization to find the cube root of 1728 is given below: Write 1728 as shown in below figure.. Take the first prime number 2 and write left of 1728 as shown in the figure.. Cube root of 27000 = 2 × 5 × 3 1. The Prime factors of number 64 are 2 which in the form of equation is expressed as: 2× 2 × 2× 2 × 2 × 2. It might take you by surprise, but the process of cubing is the same as squaring, just that the number is multiplied three times instead of two. He provides courses for Maths and Science at Teachoo. With no prior experience, Kyle Dennis decided to invest in stocks. Creating a group in triplets of the same prime, we have. Identify the product of primes, selecting one from each triplet. Thus, we denote the cube root of y by ∛y. In table of , 1728 goes 864 times so below 1728 write 864. Number 9 is divisible by 3, so add 3 to your factors. (ii) 512We see that He owes his success to 1 strategy. 2. Cube Root of 2197 by Prime Factorisation Method. Remember that all numbers not having the remainders are factors, including the divider itself. Take an example of factorization with the number 9. Another peculiarity of a number 4 is its impossibility of an algebraic equation of a greater degree than four square roots using basic arithmetic and simple operations dissolve. The Prime Factorisation of any Number Cube Root can be calculated by grouping the triplets of the same numbers. Since 5 occurs in triplets To determine the cube root of a given number, proceed as given below: Step I. write the given number as the product of primes. As an example of the cube root of 64, we denote it as 64 that gives 4³ = 4 ×4 × 4 = 64. Notice 196 = (2)(2)(7)(7) Since there is an even number of prime factors and they can be grouped in identical pairs we know that Since 64 is a perfect cube of 4, therefore, it is easy to find its cube-root by prime factorisation method. 9³ = 9 ×9 × 9 = 729 = (-9) × (-9) × (-9) = -729. Cube Root by Factorization Method Example Problems. Pro Lite, Vedantu Cube root of 10648 = 2 × 11 Prime factorization of 717 = 3x239 Cube root of 717 = (3x239)1/3 which is an irrational number. Now when we take the cube root of the given number, the identical or similar factors can be paired in a group of three. Hence, we will get the cubes of prime factors. Cube Root of a Number is the inverse of finding the cube of a number. both 2 × 2 = 4 and 2 + 2 = 4 and hence 2, NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots, NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots in Hindi, NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots (EX 7.2) Exercise 7.2, NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots (EX 7.1) Exercise 7.1, NCERT Solutions for Class 7 Science Chapter 7 Weather, Climate and Adaptations of Animals to Climate, NCERT Solutions for Class 12 Chemistry Chapter 6 General Principles and Processes of Isolation of Elements in Hindi, NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles, NCERT Solutions for Class 7 Science Chapter 7 Weather, Climate and Adaptations of Animals to Climate In Hindi, Pollution of Air and Water NCERT Solutions - Class 8 Science, NCERT Solutions of Class 6 English Chapter 1 - A Tale of Two Birds, CBSE Class 8 Maths Chapter 7 - Cubes and Cube Roots Formulas, CBSE Class 8 Maths Revision Notes Chapter 7 - Cubes and Cube Roots, CBSE Class 7 Science Revision Notes Chapter 7 - Weather, Climate and Adaptations of Animals to Climate, Class 9 Maths Revision Notes for Areas of Parallelograms and Triangles of Chapter 9, Class 10 Maths Revision Notes for Introduction to Trigonometry of Chapter 8, Class 10 Maths Areas Related to Circles Notes for Circles of Chapter 12, CBSE Class 12 Maths Chapter-8 Application of Integrals Formula, CBSE Class 7 Maths Chapter 7 - Congruence of Triangles Formulas, Vedantu