Question

Which is the smallest number, with which 600 should be multiplied so that it becomes a perfect square?

Answer 1

RESOLVING 600 INTO PRIME FACTOR , WE GET

600 = 2 X 2 X 2 X 3 X 5 X 5

GROUPING THE FACTOR INTO PAIRS

(2 X 2)X(5 X 5)X2X3

2 AND 3 IS NOT PAIR

THUS, WE MUST MULTIPLY THE NUMBER BY 2 AND 3 SO THAT THE PRODUCT IS A PERFECT SQUARE.

HENCE, THE SMALLEST NUMBER BY WHICH 600 SHOULD BE MULTIPLIEF IS 2 AND 3 .

Answer 2

6 is the smallest number, with which 600 should be multiplied so that it becomes a perfect square

Given :

The number 600

To find :

The smallest number, with which 600 should be multiplied so that it becomes a perfect square

Solution :

Step 1 of 4 :

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

600 = 2 × 2 × 2 × 3 × 5 × 5

Step 2 of 4 :

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

600 = 2² × 2 × 3 × 5²

Step 3 of 4 :

Check the number is perfect square or not

Since 2 and 3 are left over in grouping (pairs)

So the number is not a perfect square

Step 4 of 4:

Find the smallest number, with which 600 should be multiplied so that it becomes a perfect square

In order to make perfect square we need to multiply 600 with 2 & 3

Hence the required smallest number, with which 600 should be multiplied so that it becomes a perfect square

= 2 × 3

= 6

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