A-b are positive integers- If 21ab2 and 15ab are perfect squares- the minimum value of a - b is

1.If p is a factor of a perfect square, then p2 must also be a factor, where p is a prime. 21ab2 = 3.7.ab2 b2 is a perfect square. So the smallest value of a ...

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Standard VII

Mathematics

Odd and Even Numbers

a,b are posit...

Question

a,b are positive integers. If 21ab² and 15ab are perfect squares, the minimum value of a + b is

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Solution

The correct option is A
56

1.If p is a factor of a perfect square, then p² must also be a factor, where p is a prime.

21ab² = 3.7.ab²

b² is a perfect square. So the smallest value of a is 3 x 7,

∴ a = 3 x 7 = 21

15 ab = 3.5.a.b

= 3.5.3.7.b

∴ The smallest value of b is 5 x 7 = 35.

∴ a + b = 21 + 35= 56

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a,b are positive integers. If 21ab2 and 15ab are perfect squares, the minimum value of a + b is

a,b are positive integers. If 21ab² and 15ab are perfect squares, the minimum value of a + b is