Question

2.Which of the following numbers
are not perfect cubes?
O
512
O 729
O
216
O 100​

Answer 1

Answer:

100 is correct answer please mark me as brain list rate me

Answer 2

Answer : option d ) 100

Explanation:
1) Cube root of 512, 3√512 = 8
Since 512 is a perfect cube, we will use here the prime factorisation method, to get the cube root easily.
2) Step 1: Find the prime factors of 729

729 = 3 × 3 × 3 × 3 × 3 × 3

Step 2: Clearly, 729 is a perfect cube. Here we will be using laws of exponents.

729 = 36 [am × an = am+n]

729 = [32]3 [(am)n = amn]

729 = 93

Step 3: Now, we will apply cube root to both the sides of the above expression to take out the factor as a single term, which is in cubes.

3√729 = 3√(93)

So, here the cube root is cancelled by the cube of 9.

Hence, 3√729 = 9
3) Step 1: Find the prime factors of 216

216 = 2 × 2 × 2 × 3 × 3 × 3

Step 2: Clearly, 216 is a perfect cube. Therefore, group the factors of 216 in a pair of three and write in the form of cubes.

216 = (2 × 2 × 2) × (3 × 3 × 3)

216 = 23 × 33

Using the law of exponent, we get;

216 = 63 [ambm = (ab)m]

Step 3: Now, we will apply cube root on both the sides to take out the factor as a single term, which is in cubes.

3√216 = 3√(63)

So, here the cube root is cancelled by the cube of 6.

Hence, 3√216 = 6
4) 100 is not a perfect cube. Now, 1000 is a perfect cube. Thus, the required smallest number is 10.

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