find the least number by which 10368 should be (i) increased (ii) decreased(iii) multiplied (iv) divided to make it a perfect square
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Answers
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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Step-by-step explanation:
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