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Exactly $1000$ perfect squares between two consecutive cubes Therefore there are exactly $1000$ squares between the successive cubes $ (667^2)^3$ and $ (667^2+1)^3$, or between $444889^3$ and $444890^3$ Finally, we can verify all of this by using the command line utility bc: $ bc sqrt((667^2)^3) 296740963 sqrt((667^2+1)^3-1) 296741963 Cite edited Nov 27 at 22:11 community wiki 5 revs R P A reflection
definition - What is the smallest binary number of $4$ bit? Is it . . . In pure math, the correct answer is $ (1000)_2$ Here's why Firstly, we have to understand that the leading zeros at any number system has no value likewise decimal Let's consider $2$ numbers One is $ (010)_2$ and another one is $ (010)_ {10}$ let's work with the $2$ nd number $ (010)_ {10}= (10)_ {10}$ We all agree that the smallest $2$ digit number is $10$ (decimal) Can't we say $010
algebra precalculus - Which is greater: $1000^ {1000}$ or $1001^ {999 . . . The way you're getting your bounds isn't a useful way to do things You've picked the two very smallest terms of the expression to add together; on the other end of the binomial expansion, you have terms like $999^ {1000}$, which swamp your bound by about 3000 orders of magnitude
algebra precalculus - Multiple-choice: sum of primes below $1000 . . . Given that there are $168$ primes below $1000$ Then the sum of all primes below 1000 is (a) $11555$ (b) $76127$ (c) $57298$ (d) $81722$ My attempt to solve it: We know that below $1000$ there are $167$ odd primes and 1 even prime (2), so the sum has to be odd, leaving only the first two numbers
Why is 1 cubic meter 1000 liters? - Mathematics Stack Exchange 0 Can anyone explain why $1\ \mathrm {m}^3$ is $1000$ liters? I just don't get it 1 cubic meter is $1\times 1\times1$ meter A cube It has units $\mathrm {m}^3$ A liter is liquid amount measurement 1 liter of milk, 1 liter of water, etc Does that mean if I pump $1000$ liters of water they would take exactly $1$ cubic meter of space?