Question

find the smallest number by which 1008 must be multiplied so that it becomes a perfect square also find the square root of the perfect square so obtained

Answer 1

Answer:Solution :

we have 1008=2×2××2×3×3×3

The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.

Now 1008×7=2×2×2×2×3×3×7×7

7056=2×2×3×7

=84

Answer : 7

Step-by-step explanation:

Answer 2

Given:

The smallest number by which 1008 must be multiplied so that it becomes a perfect square.

To find:

The smallest number by which 1008 must be multiplied so that it becomes a perfect square also find the square root of the perfect square number

Solution:

We can find the smallest number by which 1008 must be multiplied so that it becomes a perfect square by using prime factorization method,

Prime factors of 1008,

1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7

Here, prime factor 7 has no pair.

Therefore, 1008 must be multiplied by 7 to make it perfect square.

1008 × 7 = 7056

$\sqrt{7056}$ = 84

Final answer:

The smallest number by which 1008 must be multiplied so that it becomes a perfect square is 7

The square root of the perfect square number obtained is 84