The cube root of 343 is 7.
Therefore, the cube root of 343 by prime factorization is (7 × 7 × 7)1/3 = 7.
For 343000:
Prime factorization: 343000=343×1000=73×(103)=73×(2×5)3=73×2. Cube root: 3343000 =373×23×53 =7×2×5=70.
Hence the cube root of 4913 is 17.
So, here the cube root is cancelled by the cube of 9. Hence, 3√729 = 9.
√343 = √(7 × 7 × 7) √343 = √(7) ×√(7)2. √343 = 7√7. Therefore, the square root of 343 in radical form is 7√7.
What is the Value of the Cube Root of 1331? We can express 1331 as 11 × 11 × 11 i.e. ∛1331 = ∛(11 × 11 × 11) = 11. Therefore, the value of the cube root of 1331 is 11.
The cube root of 8000 is the number which when multiplied by itself three times gives the product as 8000. Since 8000 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5. Therefore, the cube root of 8000 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5) = 20.
As 2197 is a perfect cube, it will be very easy to calculate the cube root of 2197. Therefore, = (13 * 13 * 13) = 13. Hence, the cube root of 2197 is 13. Hence, the cube root is the inverse method of determining the cube of a number.
We know, 3√343 = 7.
Hence, we have found that the cube root of 2744 is 14.
So, the prime factors of 42 are 2 × 3 × 7, where 2, 3 and 7 are prime numbers.
There are a total of 8 factors of 1001, they are 1, 7, 11,13, 77, 91, 143 and 1001. The prime factorisation of 1001 results in 7 × 11 × 13.
Therefore, the cube root of -64 × -1331 is 44.
Let's find the cube root of the number using the factorization method first we will factorize the given numbers only by the prime numbers. Hence the cube root of 10648 is 22. Hence we can say 22 is the cube root of 10648.
(See examples for 3 and 4 above.) Example: 343 is divisible by 7. Since this number, 28, is divisible by 7, (28 ÷ 7 = 4), we know that the original number, 343, is divisible by 7. Example: 12,334 is divisible by 7.
The cube root of a number is a value that, when multiplied by itself three times, gives the number. You know that 27 = 3 × 3 × 3 = 33. Hence, the cube root of 27 is 3. This can be denoted as ∛27 = 3. Finding the cube root is the inverse operation of finding the cube.
The square root of 3 is expressed as √3 in the radical form and as (3)½ or (3)0.5 in the exponent form. The square root of 3 rounded up to 7 decimal places is 1.7320508. It is the positive solution of the equation x2 = 3.
The number 729 on prime factorization gives 3 × 3 × 3 × 3 × 3 × 3. On combining the prime factors in groups of 3 gives 9. So, the cube root of 729 = ∛(3 × 3 × 3 × 3 × 3 × 3) = 9 (perfect cube).