Question

9. Find the least number by which 10368 should be (i) increased (ii) decreased (iii) multiplied
(iv) divided to make it a perfect square.​

Answer 1

Answer:

Step-by-step explanation:

10368 = 2⁷ × 3⁴

It has to be divided by 2 or multiplied by 2 to make it a perfect square.

Answer 2

Answer:

The prime factors of 10368 are:

 10368  =  2*2*2*2*2*2*2*3*3*3*3

   10368  =  ( (2*2*2)*(3*3) ) * ( (2*2*2*2)*(3*3) )

 Rule to remember:  Perfect squares have an even number of each prime factor.

 We can make a perfect square by multiplying bt 2 (the least prime factor that appears an odd number of times).

  20736 = ( (2* 2*2*2)*(3*3) ) * ( (2*2*2*2)*(3*3) )

 Or, we can divide it by 2 (the least prime factor that appears an odd number of times).

 5184 = ( (2*2*2)*(3*3) ) * ( (    2*2*2)*(3*3) )

 Since SQRT(10368) = 101.82  is between 101*101=10201  and 102*102=10404,  (the nearest perfect squares),

 we may add 36  to get 10404,

   or subtract 167 to get 10101.

NEXT STEP ( or ) ANOTHER METHOD:

Firstly we will calculate the square root of 10368 by long division method

we will left out with remainder 167.

hence 1012<103681012<10368

The next perfect square number is 1022=10404>103681022=10404>10368

I. Hence the number to be added is 10404−10368=3610404-10368=36

Thus 36 should be added to 10368 to get a perfect square.

II. since 1012<103681012<10368

so the number to subtracted is 10368−1012=10368−10201=16710368-1012=10368-10201=167

Therefore, 167 should be subtracted from 10368 to make it  a perfect square.

III. Prime factorization of 10368 is 2×2×2×2×2×2×2×3×3×3×32×2×2×2×2×2×2×3×3×3×3  

Therefore 10368 should be multiplied by 2 to make it a perfect square

and 10368 should be divided by 2 to make it a perfect square

Step-by-step explanation:

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