Question

Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:

a) 1800

b)14283

c)2904

Answer 1

heya
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[ first of all we need to find the prime factors of the numbers ]

ⓐ 1,800

Prime Factors of 1,800
= 5×5×3×3×2×2×2

Smallest no. to be divided = 2
[ as 2 is not in pair ]

So, 1,800/2 = 5×5×3×3×2×2×2/2

♦ √900
= √5×5×3×3×2×2
= 5×3×2
= 30

♢ Perfect sq. = 900
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ⓑ 14,283

Prime factors of 14,283
= 23×23×3×3×3

Smallest no. to be divided = 3
[ as 3 is not in pair ]

So, 14,283/3 = 23×23×3×3×3/3

♦ √4761
= √23×23×3×3
= 23×3
= 69

♢ Perfect sq. = 4761
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ⓒ 2904

Prime factors of 2904
= 11×11×2×2×2×3

Smallest no. to be divided = 2×3 = 6
[ as 2 & 3 are not in pair ]

So, 2904/6 = 11×11×2×2×2×3/6

♦ √484
= √11×11×2×2
= 11×2
= 22

♢ Perfect sq. = 484
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I hope this answer helps you !

Answer 2

HELLO MATES ❤

Refer to attachment ⬆️

MARK AS BRAINLIEST