The number 1728 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. On combining the prime factors in groups of 3 gives 12. So, the cube root of 1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12 (perfect cube).
Hence, the cube root of 1728 is 12.
Prime factorisation of 1728=26×33. So, number of factors =(6+1)(3+1)=28.
Cube root of a number can be found by a very simple method which is the prime factorization method. Cube root is denoted by '∛ ' symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2.
What is the Square Root of 1728? The square root of 1728, (or root 1728), is the number which when multiplied by itself gives the product as 1728. Therefore, the square root of 1728 = √1728 = 24 √3 = 41.569219381653056.
Cube root of 1728, 3√1728 = 12
Thus, we can use an estimation method for fast calculation.
So, cube root of 175616 is 56.
In order to find the prime factorization of the number, we continuously divide the number with prime numbers. Further simplifying the RHS and writing it in the form of a cube. Hence, the cube root of 13824 is 24.
Answer: The cube root of 27000 is 30. We must use the prime factorisation method to obtain the cube root of 27000. 27000 = (2*2*2)(3*3*3)(5*5*5) by arranging the elements into triplets of equal factors. 27000 can be divided into equal-factor triplets in this case.
Thus, the prime factorization of 1729 is \[1729=7\times 13\times 19\]. So, the prime factors of 1729 are 7, 13 and 19. We observe that they are already arranged in ascending order.
When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number. For example, we can write the number 72 as a product of prime factors: 72 = 2 3 ⋅ 3 2 . The expression 2 3 ⋅ 3 2 is said to be the prime factorization of 72.
The cube root of 1729 is the number which when multiplied by itself three times gives the product as 1729. Since 1729 can be expressed as 7 × 13 × 19. Therefore, the cube root of 1729 = ∛(7 × 13 × 19) = 12.0023.
The factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728 and factors of 631 are 1, 631.
The cube root of – 17567, i.e. -$\sqrt[3]{{ 17576}}$= -26. Note: In order to solve such types of problems the key is to express the given number as a product of prime numbers, then we rewrite all its factors until we achieve a number raised to the power 3 as we are supposed to find the cube root.
= 5 × 7 = 35. Q.
In order to find the answer, first we take the number without the decimal that is equal to 1331 and by prime factorization we will get to know that the cube root of 1331 is equal to 11. Similarly in the same way we observe that the cube root of 1.331 is equal to 1.1.
We search for the largest cube number which is less than the number in the second group. So the ten's digit of cube root of 4913 is 1. Hence the cube root of 4913 is 17.
Hence, the cube root of \[12167\] is \[23\] by prime factorization method. Note: When prime numbers are multiplied by any natural or whole number (except 0), composite numbers are generated. Essentially, prime factorization is used to factorise and locate prime factors for composite numbers.
Answer: The cube root of 636056 is 86.
The base 12 logarithm of 1728 is 3. The base 12 logarithm of 1728 is 3.
Thus we have to multiply 1728 by 3 to make it a perfect square. = 5184, a perfect square of 72. Answer. 3 is the smallest number by which 1728 must be multiplied to make it a perfect square.
1728 can be expressed as 12³