Question

12 By which smallest no must the following
numbers be divided so that the quotions
is a betect square
a) 675 b) 8640 c) 1600 d) 8788
e) 7803​

Answer 1

$\bold \red{answer}$

i) 675

675 = 3 × 3 × 3 × 5 × 5 = 33 × 52

Since 675 is not a perfect cube.

To make the quotient a perfect cube we divide it by 52 = 25, which gives 27 as quotient where, 27 is a perfect cube.

∴ 25 is the required smallest number.

(ii) 8640

8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 = 23 × 23 × 33 × 5

Since 8640 is not a perfect cube.

To make the quotient a perfect cube we divide it by 5, which gives 1728 as quotient and we know that 1728 is a perfect cube.

∴5 is the required smallest number.

(iii) 1600

1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 = 23 × 23 × 52

Since 1600 is not a perfect cube.

To make the quotient a perfect cube we divide it by 52 = 25, which gives 64 as quotient and we know that 64 is a perfect cube

∴ 25 is the required smallest number.

(iv) 8788

8788 = 2 × 2 × 13 × 13 × 13 = 22 × 133

Since 8788 is not a perfect cube. To make the quotient a perfect cube we divide it by 4, which gives 2197 as quotient and we know that 2197 is a perfect cube

∴ 4 is the required smallest number.

(v) 7803

7803 = 3 × 3 × 3 × 17 × 17 = 33 × 172

Since 7803 is not a perfect cube.

To make the quotient a perfect cube we divide it by 172 = 289, which gives 27 as quotient and we know that 27 is a perfect cube

∴ 289 is the required smallest number

Answer 2

Step-by-step explanation:

factors of 675= 3×3×3×5×5

here, 3 does not have it's pair.

hence 675 must be divided by 3 to get a perfect square.

675÷3= 225

225 is a perfect square of 15..