The prime factorization of 792 is 2 x 2 x 2 x 3 x 3 x 11.

The orange divisor(s) above are the prime factors of the number 5,625. If we put all of it together we have the factors 3 x 3 x 5 x 5 x 5 x 5 = 5,625.

According to the definition of factors, the factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. So,126 is a composite number as it has factors other than 1 and itself.

5

15

So, Therefore 17 is a smallest number by which the 7803 is multiplied to become a perfect cube.

Answer: Hence 5 is the smallest number by which 48640$ must be divided so that the quotient is a perfect cube.

36

A: Yes, the number 26,244 is a perfect square.

The orange divisor(s) above are the prime factors of the number 26,244. If we put all of it together we have the factors 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 26,244. It can also be written in exponential form as 22 x 38.

We will divide this number by the lowest possible natural number, then whatsoever the quotient will remain, we will see by which number that number will get divisible. In this way, we will divide till we get the quotient as 1. Hence, we have found the cube root of 6859 as 19.

6859 is said to be a perfect cube because 19 x 19 x 19 is equal to 6859. Since 6859 is a whole number, it is a perfect cube. The nearest previous perfect cube is 5832 and the nearest next perfect cube is 8000 . 6859 is said to be a perfect cube because 19 x 19 x 19 is equal to 6859.

6,859 is not divisible by any number less than or equal to 9.

Therefore, the required cube root of 15625 is 25. Note: Here, after prime factorisation, you will get prime factors. Now, to obtain the cube root, take the similar numbers in groups of three and one factor from each group should be taken and then multiply all such factors.

The square root of 1728 rounded up to 6 decimal places is 41.569219….Square Root of 1728.

It is quite easy to find the cube root of 1728 as it is a perfect cube. Hence, the cube root of 1728 is 12.

3

We know that the cube root of negative numbers is negative. Hence, the cube root of -64 is -4.

Example – Find the cubed root of 512 using trial and error: Try a number – 5 : 5 x 5 x 5 = 125 (too low)

Exponent Tables and Patterns

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