Question

Test whether the given numbers are perfect cubes or not.
(i) 243
(ii) 516
(iii) 729
(iv) 8000
(v) 2700

Answer 1

Perfect cubes ⇒ When the number can be represented in the form of another integer(s) with exponents in the multiples of 3s

Find the prime factors:

(i) 243  = 3⁵ (exponent ≠ multiple of 3s≠ not a perfect cube)

(ii) 516 = 2² x 3 x 43 (exponent ≠ multiple of 3s≠ not a perfect cube)

(iii) 729 = 3⁶ (exponent = multiple of 3 = perfect cube)

(iv) 8000 = 2⁶ x 5³ (exponent = multiple of 3 = perfect cube)

(v) 2700 = : 2² x 3³ x 5²(exponent ≠ multiple of 3s≠ not a perfect cube)

Answer: 729 and 8000 are perfect cubes

Answer 2

Answer:

1: not a perfect cube

2: not a perfect cube

3: perfect cube

4: perfect cube

5:not a perfect cube