Question

find the smallest numberby which 9408 must be divided so that it becomes a perfect square. also find the square root of the number so obtained.

Answer 1

9408= 2*2*2*2*2*2*3*7

If we divide 9408 by factor 3, then

9408/3+ 3136 = 2*2*2*2*2*2*7*7. Which is perfect square.

Therefor required smallest no. is 3. And

square root of 3136 = 3*3*3*7 = 56

Answer 2

Here is your answer..

Solution :

9408 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 3

We observe that prime factor 3 doesn't form a pair.

Therefore, We must divide the number 3 so that the quotient becomes a perfect square.

: 9408/3 = 3136

3136 = ( 2 × 2 ) × ( 2 × 2 ) ( 2 × 2 ) ( 7 × 7 )

Now, each prime factor occurs in pairs. Therefore, the required smallest number is 3.

: √3136 = 2 × 2 × 2 × 7 × = 56


Hope it helped ☺☺☺