Question

The smallest no. by which 150 should be divided so as to get a perfect square is​

Answer 1

150 = 2 x 3 x 5 x 5

we can see that the digit 5 is in pair but not the digits 2 and 3. so we need to remove them to find perfect square.

so our answer is 2 x 3 = 6

we need to divide 150 by 6 to a perfect square.

Answer 2

SOLUTION

TO DETERMINE

The smallest no. by which 150 should be divided so as to get a perfect square

CONCEPT TO BE IMPLEMENTED

Step : I

Firstly express the given number as a product of prime factor by using prime factorisation

Step : II

Make the pair of similar factors such that the both factors in each pair are equal.

Step : III

Take one factor from each pair.

Step : IV

If no factor is left over in grouping (pairs) then the number is perfect square otherwise not

Step : V

If no factor left find the product of factor that obtained by taking one factor from each pair. That product is the square root of the given number.

EVALUATION

Here the given number = 150

We now prime factorise the given number

150 = 2 × 3 × 5 × 5 = 2 × 3 × 5²

We see that only 5 is in pair form . 2 and 3 is left over in grouping (pairs)

Now 2 × 3 = 6

In order to get a perfect square we must have to divide 150 by 6

Then the newly obtained number 25 is a perfect square

Hence the required number = 6

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