There are 20 non - perfect square numbers between the square of x and y. If x and y are two consecutive natural numbers, then find the value of x and y.

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Solution

Dear student
$G i v e n x a n d y a r e c o n s e c u t i v e n a t u r a l n u m b e r s . S i n c e i t i s g i v e n t h a t t h e r e a r e 20 n o n - p e r f e c t s q u a r e s n u m b e r s b e t w e e n t h e s q u a r e o f x a n d y . B e t w e e n 1^{2} a n d 2^{2} t h e r e a r e 2 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 2^{2} a n d 3^{2} t h e r e a r e 4 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 3^{2} a n d 4^{2} t h e r e a r e 6 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 4^{2} a n d 5^{2} t h e r e a r e 8 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 5^{2} a n d 6^{2} t h e r e a r e 10 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 6^{2} a n d 7^{2} t h e r e a r e 12 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 7^{2} a n d 8^{2} t h e r e a r e 14 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 8^{2} a n d 9^{2} t h e r e a r e 16 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 9^{2} a n d 10^{2} t h e r e a r e 18 n o n - p e r f e c t s q u a r e n u m b e r s . B e t w e e n 10^{2} a n d 11^{2} t h e r e a r e 20 n o n - p e r f e c t s q u a r e n u m b e r s . S o, t h e v a l u e o f x a n d y i s 10 a n d 11 r e s p e c t i v e l y .$
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Similar questions

How many non-perfect square numbers are there between the squares of 20 and 21?

The number of non-perfect square numbers between the squares of two consecutive integers n and (n + 1) is __________.

n

(n + 1)

(n + 1)^{2}

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