How many numbers from 1 to 1 million are not perfect squares or perfect cubes?
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OpenStudy (akshay_budhkar):
difficult one
OpenStudy (anonymous):
is there an equation to solve this?
OpenStudy (anonymous):
I'm actually interested
OpenStudy (anonymous):
less than a million. More than just one. :P
OpenStudy (akshay_budhkar):
lol
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OpenStudy (anonymous):
I Shall figure it out !
OpenStudy (akshay_budhkar):
you asking this for fun right?
OpenStudy (anonymous):
yeah
OpenStudy (anonymous):
998,910
OpenStudy (akshay_budhkar):
OMG!
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OpenStudy (anonymous):
1 mill - 1100 +10
OpenStudy (anonymous):
u are right answer is 998910
OpenStudy (anonymous):
for every integer from 1 to 1000 there is an n^2 less than 1,000,000. Therefore, there are 1000 perfect squares
for every integer from 1 to 100 there is an n^3 less than 1,000,000. Therefore, there are 100 perfect cubes.
there are 10 perfect squares that are also perfect cubes. 1^6, 2^6, 3^6...to 10^6.
Thus there are 1000+100-10=1090 distinct numbers that are perfect squares and perfect cubes.
Thus there are 998910 numbers not perfect squares or cubes