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▶Find the smallest number by which 1800 must be divided so that the quotient is a perfects square? Find the square root of the quotient?
▶Navya makes a cuboid of plasticine of sides 7cm,2cm,7cm. How many such cuboidal will she need to form a cube?
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Answers
(1)
Prime factorization of 1800 = 2 * 2 * 2 * 3 * 3 * 5 * 5
⇒ Here, Prime factor 2 is not in a pair. To get a perfect square, 1800 is divided by 2.
⇒ 1800/2 = 900
= 2 * 2 * 3 * 3 * 5 * 5
= 2 * 3 * 5
= 30.
Therefore,
⇒ The smallest number to be divided = 2.
⇒ The square root of the Quotient = 30.
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(2)
Length of each edge of cube = LCM of 7 and 2.
⇒ Prime factorization of 7 = 7
⇒ Prime factorization of 2 = 2
Hence, LCM(7,2) = 7 * 2
= 14.
Now,
⇒ Number of cuboids = (Volume of a cube)/(Volume of cuboid)
= (14)^3/(7 * 2 * 7)
= 2744/98
= 28.
Therefore, Number of cuboids = 28.
Hope this helps!