Find the smallest number by which it must be divided to make it a perfect square. Also find the square rool of the number so obtained. 4050
Answers
Step-by-step explanation:
A number is a perfect square when we get even number of each prime factor on its factorization.
(a).4050=2×5×5×3×3×3×3
2 exists only 1 (odd) time.
Thus, the number is to be divided by 2 to get a perfect square.
5×5×3×3×3×3=2025
∴
2025
=5×3×3=45
(b).17328=4×4×19×19×3
3 exists only 1 (odd) time.
Thus, the number is to be divided by 3 to get a perfect square.
4×4×19×19=5776
∴
5776
=4×19=76
(c).53016=2×2×2×3×47×47
2 and 3 exists only 1 (odd) time.
Thus, the number is to be divided by the smallest of 2 and 3 i.e. 2 to get a perfect square.
2×2×47×47=8836
∴
8836
=2×47=94
(d).38440=5×2×2×2×31×31
5 and 2 exists only 1 (odd) time.
Thus, the smallest number is 5×2=10 by which the number is to be divided to get a perfect square.
2×2×31×31=3844
∴
3844
=2×31=62
(e).5832=2×2×2×3×3×3×3×3×3
3 exists only 3 (odd) times.
Thus, the number is to be divided by 3 to get a perfect square.
2×2×3×3×3×3×3×3=2916
∴
2916
=3×3×3×2=54