Question

Find the number of positive integers n is less than or equal to 1000 such that 15n is a perfect square.

Answer 1

Answer:

8 positive integers.

Step-by-step explanation:

One value of n would be 15 because 225 = 15^2.

Other values  are 225 * n where 15n  <= 1000 and n is a perfect square.

So n = 4 gives us 225* 4 = 900 which is a perfect square and 15*4 = 60.

n = 9  gives us 225 * 9 which is a perfect square and 15*9 = 135.

n = 16 gives us 225*16  and 15*16 = 240 , so OK.

n = 25   gives a perfect square and  and 15*25 = 375 - so OK.

n = 36 gives a perfect square and 15*36 = 540 - so OK.

n = 49 gives a perfect square and  15*49 = 735 - so OK.

n = 64 gives a perfect square and 15*64 = 960 - so ok.

n = 81 gives a perfect square and 15 * 81 = 1215  so NOT ok.