Mixing
How to find the number of squares between a range of numbers that are also divisible by $ 12 $?
$begingroup$
I know to find all numbers divisible by $ 12 $ between a range of numbers is something like:
$$ frac{x}{12} - frac{y}{12} + 1, quad text{where} x>y .$$
And to find the number of squares would be:
$$left lfloor{sqrt{y}} rightrfloor- left lceil {sqrt{x}} right rceil + 1$$
Is there some way to calculate the number of numbers that has both qualities?
algebra-precalculus
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
asked Jan 23 at 2:12
Kevin LeKevin Le
1
$endgroup$
add a comment |
$begingroup$
I know to find all numbers divisible by $ 12 $ between a range of numbers is something like:
$$ frac{x}{12} - frac{y}{12} + 1, quad text{where} x>y .$$
And to find the number of squares would be:
$$left lfloor{sqrt{y}} rightrfloor- left lceil {sqrt{x}} right rceil + 1$$
Is there some way to calculate the number of numbers that has both qualities?
algebra-precalculus
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
asked Jan 23 at 2:12
Kevin LeKevin Le
1
$endgroup$
$begingroup$
Welcome to MSE! Can you provide some context? See: math.meta.stackexchange.com/questions/9959/…
$endgroup$
– user549397
Jan 23 at 2:34
add a comment |
$begingroup$
I know to find all numbers divisible by $ 12 $ between a range of numbers is something like:
$$ frac{x}{12} - frac{y}{12} + 1, quad text{where} x>y .$$
And to find the number of squares would be:
$$left lfloor{sqrt{y}} rightrfloor- left lceil {sqrt{x}} right rceil + 1$$
Is there some way to calculate the number of numbers that has both qualities?
algebra-precalculus
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
asked Jan 23 at 2:12
Kevin LeKevin Le
1
$endgroup$
I know to find all numbers divisible by $ 12 $ between a range of numbers is something like:
$$ frac{x}{12} - frac{y}{12} + 1, quad text{where} x>y .$$
And to find the number of squares would be:
$$left lfloor{sqrt{y}} rightrfloor- left lceil {sqrt{x}} right rceil + 1$$
Is there some way to calculate the number of numbers that has both qualities?
algebra-precalculus
algebra-precalculus
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
asked Jan 23 at 2:12
Kevin LeKevin Le
1
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
asked Jan 23 at 2:12
Kevin LeKevin Le
1
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
edited Jan 23 at 5:42
J. W. Tanner
3,1061320
3,1061320
asked Jan 23 at 2:12
Kevin LeKevin Le
1
asked Jan 23 at 2:12
Kevin LeKevin Le
1
asked Jan 23 at 2:12
Kevin LeKevin Le
1
1
$begingroup$
Welcome to MSE! Can you provide some context? See: math.meta.stackexchange.com/questions/9959/…
$endgroup$
– user549397
Jan 23 at 2:34
add a comment |
$begingroup$
Welcome to MSE! Can you provide some context? See: math.meta.stackexchange.com/questions/9959/…
$endgroup$
– user549397
Jan 23 at 2:34
$begingroup$
Welcome to MSE! Can you provide some context? See: math.meta.stackexchange.com/questions/9959/…
$endgroup$
– user549397
Jan 23 at 2:34
$begingroup$
Welcome to MSE! Can you provide some context? See: math.meta.stackexchange.com/questions/9959/…
$endgroup$
– user549397
Jan 23 at 2:34
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
To be a square divisible by $12$ a number needs to be divisible by $36$ because you need an even number of factors of $3$. The square root then needs to be divisible by $6$. So find the number of numbers divisible by $6$ between $lceil sqrt x rceil$ and $lfloor sqrt yrfloor$ inclusive
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3083992%2fhow-to-find-the-number-of-squares-between-a-range-of-numbers-that-are-also-divis%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
To be a square divisible by $12$ a number needs to be divisible by $36$ because you need an even number of factors of $3$. The square root then needs to be divisible by $6$. So find the number of numbers divisible by $6$ between $lceil sqrt x rceil$ and $lfloor sqrt yrfloor$ inclusive
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
$endgroup$
add a comment |
$begingroup$
To be a square divisible by $12$ a number needs to be divisible by $36$ because you need an even number of factors of $3$. The square root then needs to be divisible by $6$. So find the number of numbers divisible by $6$ between $lceil sqrt x rceil$ and $lfloor sqrt yrfloor$ inclusive
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
$endgroup$
add a comment |
$begingroup$
To be a square divisible by $12$ a number needs to be divisible by $36$ because you need an even number of factors of $3$. The square root then needs to be divisible by $6$. So find the number of numbers divisible by $6$ between $lceil sqrt x rceil$ and $lfloor sqrt yrfloor$ inclusive
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
$endgroup$
To be a square divisible by $12$ a number needs to be divisible by $36$ because you need an even number of factors of $3$. The square root then needs to be divisible by $6$. So find the number of numbers divisible by $6$ between $lceil sqrt x rceil$ and $lfloor sqrt yrfloor$ inclusive
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
answered Jan 23 at 2:20
Ross MillikanRoss Millikan
299k24200374
299k24200374
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3083992%2fhow-to-find-the-number-of-squares-between-a-range-of-numbers-that-are-also-divis%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Welcome to MSE! Can you provide some context? See: math.meta.stackexchange.com/questions/9959/…
$endgroup$
– user549397
Jan 23 at 2:34