Question

Find the least number by which 69192 must be (i) increased (ii) decreased (iii) multiplied (iv) divided ,to make it a perfect square

Answer 1

Answer:

i) The least increased number to make it a perfect square is 504.

ii) The least decreased number to make it a perfect square is 23.

iii)The least multiplied number  to make it a perfect square is 2.

iv) The least divide number to make it a perfect square is 2.          

Step-by-step explanation:

Given : Number 69192.

To find : The least number by which 69192 must be

(i) increased (ii) decreased (iii) multiplied (iv) divided ,to make it a perfect square.

Solution :

For (i) and (ii),

We find the number in between the number square root lie.

$\sqrt{69192}=263.04$

i.e. $263^2< 69192<264^2$

(i) For increased number,

Subtract 69192 from $264^2$

i.e. $264^2-69192=69696-69192=504$

Therefore, The least increased number to make it a perfect square is 504.

(ii) For decreased number,

Subtract  $263^2$ from 69192

i.e. $69192-263^2=69192-69169=23$

Therefore, The least decreased number to make it a perfect square is 23.

For (iii) and (iv),

We find the factor of the number.

$69192=2\times 2\times 2\times 3\times 3\times 31\times 31$

(iii) For multiplied,

If we see the pairs only one 2 is left alone.

So, If we multiply it with 2 it will make a perfect square.

Therefore, The least multiplied number  to make it a perfect square is 2.

(iv) For divided,

If we see the pairs only one 2 is left alone.

So, If we divide it with 2 it will make a perfect square.

Therefore, The least divide number to make it a perfect square is 2.

Answer 2

Step-by-step explanation:

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