Exponents Powers Test

Result

Exponents Powers Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following expressions is not a perfect cube?

A
25 × 10 × 32

B
125 × 8 × 125

C
15 × 8 × 25 × 9

D
49 × 21 × 27 × 8

Solution

When we will factorize the expressions given in alternatives A, B, C, we will see that in these expressions, the prime factors appear in group of three. No factor will be there which does not appear in the group of three.

So the expressions given in alternatives A, B, C are perfect squares

Now consider the expression given in alternative D which is 49 ×21 ×27 ×8 .

We can factorize it as

49 ×21 ×27 ×8 = (7 ×7) ×(3 ×7) ×(3 ×3 ×3) ×(2 ×2 ×2)

= 7 ×7 ×7 × 3 ×3 ×3 ×3 × 2 ×2 ×2

We see that the prime factor 3 does not appear in a group of three.

Thus, 49 ×21 ×27 ×8 is not a perfect cube.
Question 2
1 / -0

What is the smallest number by which 6468 is to be divided so that the number obtained becomes a perfect square?

A
3

B
7

C
19

D
33

Solution

We start by prime factorizing the number 6468. The number 6468 can be factorized as:

2 6468

2 3234

3 1617

7 539

7 77

11

It can be seen that the prime factors 3 and 11 do not occur in pairs.∴ 6468 = 2 × 2 × 3 × 7 × 7 × 11

Therefore, if we divide 6468 by (3 × 11) = 33, we get 2 × 2 × 7 × 7 = 196, which is a perfect square.

Thus, the required number is 33.