Any root of is . if we find the prime factorization of 73002, we will get 23 x 23 x 23 x 2 x 3. Simplify cube root of 1/343. What will be the smallest number with which you can multiply 43904 to make it a perfect cube. For example, we want to see if 243 is a perfect cube or not? Pull terms out from under the radical, assuming real numbers. 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Definition of cube root. A cube which is a solid figure has all its sides equal if we take a measurement. The result can be shown in multiple forms. Tap for more steps... Rewrite as . Solution 1) The first we do is find the prime factorization, So the prime factorization of 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3, = (2 x 2 x 3) x (2 x 2 x 3) x (2 x 2 x 3). Step 6: Determine the rest of your divisors and do the same for the next. Example 5) What can be the smallest number by which 73002 be divided to make a perfect cube? A cube root of a number a is a number x such that x 3 = a, in other words, a number x whose cube is a. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. Exact Form: Decimal Form: This is the basic definition of the cube root.Suppose, ‘n’ is the value of 3 √343, then n × n × n = n 3 = 343. So, 7 x 7 x 7 = 343. As you can see the radicals are not in their simplest form. We can also check if a number is a perfect cube or not. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. 9 x 9 x 9 = 729. References [1] Weisstein, Eric W. "Cube Root." Here, there is already a group of three 23s but 2 and 3 are left. Therefore, 243 is not a perfect cube. Solution 6) We can find the cube of 27 by multiplying it three times i.e., 27 x 27 x 27 = 19683. Sorry!, This page is not available for now to bookmark. Solution 3) The factors of 15625 are 5 x 5 x 5 x 5 x 5 x 5. Pro Lite, Vedantu The nearest previous perfect cube is 216 and the nearest next perfect cube is 512 . Some common roots include the square root, where n = 2, and the cubed root, where n = 3. Step 3: Think of a number that you can cube to produce the largest possible result but it should be less than than the first three numbers in the set. What is Cube Root of 343 ? Solution 4) If we find out the prime factorization of 43904, our result will be: So we can make two groups of 2s, each consisting of three 2s and next there is already a group consisting of three 7s. In mathematics, the general root, or the n th root of a number a is another number b that when multiplied by itself n times, equals a. For example, 7 is the cube root of 343 because 7 3 = 7•7•7 = 343, -7 is cube root of -343 because (-7) 3 = (-7)•(-7)•(-7) = -343. If we find out the factors of 9261, we will see that 3 x 3 x 3 x 7 x 7 x 7 are the factors of 9261. Answer: Yes we can find cube root of 343 by hand but there are a few steps that will make it easy for you. That is (2 x 2 x 2) x (2 x 2 x 2) x (7 x 7 x 7). Cube of ∛343=7 which results into 7∛1; All radicals are now simplified. Now extract and take out the cube root ∛343 * ∛1. The cube root of 343, denoted as 3 √343, is a value which gives the original value when we multiply it three times by itself. Example 4) What will be the smallest number with which you can multiply 43904 to make it a perfect cube. Yes we can find cube root of 343 by hand but there are a few steps that will make it easy for you. Here, 343 is the cube of 7, and 7 is the cube root of 343. So, if we divide the number by 6, a perfect cube can be achieved. Solution 2) If we find out the factors of 9261, we will see that 3 x 3 x 3 x 7 x 7 x 7 are the factors of 9261. In doing this, one 2 is left therefore in order to make a perfect cube, we need to more 2s i.e., it should be multiplied by 4. In this article, we will find the value of n, using the prime factorisation method. If we multiply 9 three times to itself, the product will be 729. Let's check this with ∛343*1=∛343. The symbol that we use to represent a cube root is the same as that of a square root with the only difference that in a square root, we use the number 2 and in cube root, we use the number 3. Step 2: Know the cube of every single number Step 3: Think of a number that you can cube to produce the largest possible result but it should be less than than the first three numbers in the set. If we break down 243 as 3 x 3 x 3 x 3 x 3, we will see that it has five 3s and in a perfect cube, a group is made of three number that are equal. In this case, we can only make one group consisting of three 3s and we will be left with two extra 3s. Now let’s consider the number 7. Here, 25 is the square of 5, and 5 is the square root of 25. The prime factorization of 27 will be: In a square root, we always multiply the number twice to itself whereas, in a cube root, we have to multiply a number thrice to itself. It is better if we start with an example before trying to understand its formal definition.