Question

Find the smallest number by which 1920 should've divided to get a perfect square .find the square root of new number obtained

Answer 1

Step-by-step explanation:

STEP 1:FACTORISE

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

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

= 120

STEP 2:NOW DIVIDE:

1920/120

=16 ( SQUARE NUMBER )

ITS SQUARE ROOT IS 4

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Answer 2

• 30 is the smallest number by which the number 9680 must be divided to make a perfect square

• The square root of new number obtained = 8

Given :

The number 1920

To find :

The smallest number by which we divide the number 1920 to make a perfect square

The square root of the new number obtained

Concept :

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

Solution :

Step 1 of 3 :

Prime factorise the given number

Here the given number is 1920

1920 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5

∴ 1920 = 2² × 2² × 2² × 2 × 3 × 5

Step 2 of 3 :

Find the smallest number by which the number 9680 must be divided to make a perfect square

Since the factors 2 , 3 , 5 do not have pair

Now , 2 × 3 × 5 = 30

So we need to divide the number 1920 by 30 to make a perfect square

Hence 30 is the smallest number by which the number 1920 must be divided to make a perfect square

Step 3 of 3 :

Find the square root of the new number obtained

The new number obtained

= 1920/30

= 64

Hence the square root of the new number obtained

= √64

= 8

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