Question

Which of the following numbers are not perfect cubes?

 (i) 216

(ii) 128

(iii) 1000

(iv) 100

(v) 46656


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Answer 1

Answer:

Step-by-step explanation:

(i) 216 is the cube of 6

(iii) 1000 is the cube of 10

(v) 46656 is the cube of 36

therefore 100 and 128 are not perfect cubes

Answer 2

★ To Find :-

• Which of the following numbers are not perfect cubes?

Let's understand the concept first :-

To check whether the numbers are perfect cubes or not just we need to know some important points :-

★ Using prime factorization method .

Now, the question arises what is prime factorization method ?

• Prime factorization Method is a method of factoring the given number in prime number form . Therefore, all the factors will be prime numbers.

★ Make pair of 3 numbers.

★ If after making pairs of 3 - 3 prime factors , no other factor is left then it is definitely a perfect cube.

Now, let's do the questions :-

i) 216

Factors = 2 × 2 × 2 × 3 × 3 × 3

↬ Hence, two pairs are formed 2³ × 3³ and no other factors left.

↬ 216 is a perfect cube.

ii) 128

Factors = 2 × 2 × 2 × 2 × 2 × 2 × 2

↬ 2³ × 2³ Here, after making two pairs one factor 2 is left .

↬ Therefore, 218 is not a perfect cube.

iii) 1000

Factors - 10 × 10 × 10

↬ One pair formed 10³ and no other factor left.

↬ 1000 is a perfect cube.

iv) 100

Factors = 10 × 10

↬ Here it's not making pair of three

↬ Hence, 100 is not a perfect cube.

v) 46656

Factors = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

↬2³ × 2³ × 3³ × 3³

↬ 4 pairs formed and no other factor left$.$

↬ So, 46656 is a perfect cube.

Then ,

➤ The numbers which are not perfects cubes are :-

ii) 128

iv) 100

➤ The perfect cubes are as following :-

I) 216

iii) 1000

v) 46656

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