How to convert any decimal number in form of $sqrt a+sqrt b$?
0
$begingroup$
Is there any method to directly convert any decimal number in form of $sqrt a+sqrt b$, given a and b are integers? Like $4.88=sqrt5+sqrt7$ (approximately)
irrational-numbers
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
asked Dec 2 '18 at 3:14
marthamartha
71
$endgroup$
add a comment |
0
$begingroup$
Is there any method to directly convert any decimal number in form of $sqrt a+sqrt b$, given a and b are integers? Like $4.88=sqrt5+sqrt7$ (approximately)
irrational-numbers
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
asked Dec 2 '18 at 3:14
marthamartha
71
$endgroup$
1
$begingroup$
$4.88 neq sqrt 5 + sqrt 7$ LHS is rational, RHS is irrational. If you'd written $4.88 approx sqrt 5 + sqrt 7$ that would be acceptable.
$endgroup$
– Deepak
Dec 2 '18 at 3:16
$begingroup$
@martha Do you mean to convert any rational number?
$endgroup$
– Toby Mak
Dec 2 '18 at 3:41
2
$begingroup$
If $r=sqrt a+sqrt b$, then $rgesqrt a$, so $ale r^2$, and similarly $ble r^2$. So if worst comes to worst you can just check every pair $(a,b)$ up to $r^2$ to see which one comes closest. Not quite as bad as it sounds, as for each value of $a$ that you try, you can compute $(r-sqrt a)^2$ to see what value of $b$ to try.
$endgroup$
– Gerry Myerson
Dec 2 '18 at 3:48
add a comment |
0
0
0
$begingroup$
Is there any method to directly convert any decimal number in form of $sqrt a+sqrt b$, given a and b are integers? Like $4.88=sqrt5+sqrt7$ (approximately)
irrational-numbers
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
asked Dec 2 '18 at 3:14
marthamartha
71
$endgroup$
Is there any method to directly convert any decimal number in form of $sqrt a+sqrt b$, given a and b are integers? Like $4.88=sqrt5+sqrt7$ (approximately)
irrational-numbers
irrational-numbers
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
asked Dec 2 '18 at 3:14
marthamartha
71
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
asked Dec 2 '18 at 3:14
marthamartha
71
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
edited Dec 2 '18 at 7:21
Tianlalu
3,08121038
3,08121038
asked Dec 2 '18 at 3:14
marthamartha
71
asked Dec 2 '18 at 3:14
marthamartha
71
asked Dec 2 '18 at 3:14
marthamartha
71
71
1
$begingroup$
$4.88 neq sqrt 5 + sqrt 7$ LHS is rational, RHS is irrational. If you'd written $4.88 approx sqrt 5 + sqrt 7$ that would be acceptable.
$endgroup$
– Deepak
Dec 2 '18 at 3:16
$begingroup$
@martha Do you mean to convert any rational number?
$endgroup$
– Toby Mak
Dec 2 '18 at 3:41
2
$begingroup$
If $r=sqrt a+sqrt b$, then $rgesqrt a$, so $ale r^2$, and similarly $ble r^2$. So if worst comes to worst you can just check every pair $(a,b)$ up to $r^2$ to see which one comes closest. Not quite as bad as it sounds, as for each value of $a$ that you try, you can compute $(r-sqrt a)^2$ to see what value of $b$ to try.
$endgroup$
– Gerry Myerson
Dec 2 '18 at 3:48
add a comment |
1
$begingroup$
$4.88 neq sqrt 5 + sqrt 7$ LHS is rational, RHS is irrational. If you'd written $4.88 approx sqrt 5 + sqrt 7$ that would be acceptable.
$endgroup$
– Deepak
Dec 2 '18 at 3:16
$begingroup$
@martha Do you mean to convert any rational number?
$endgroup$
– Toby Mak
Dec 2 '18 at 3:41
2
$begingroup$
If $r=sqrt a+sqrt b$, then $rgesqrt a$, so $ale r^2$, and similarly $ble r^2$. So if worst comes to worst you can just check every pair $(a,b)$ up to $r^2$ to see which one comes closest. Not quite as bad as it sounds, as for each value of $a$ that you try, you can compute $(r-sqrt a)^2$ to see what value of $b$ to try.
$endgroup$
– Gerry Myerson
Dec 2 '18 at 3:48
1
1
$begingroup$
$4.88 neq sqrt 5 + sqrt 7$ LHS is rational, RHS is irrational. If you'd written $4.88 approx sqrt 5 + sqrt 7$ that would be acceptable.
$endgroup$
– Deepak
Dec 2 '18 at 3:16
$begingroup$
$4.88 neq sqrt 5 + sqrt 7$ LHS is rational, RHS is irrational. If you'd written $4.88 approx sqrt 5 + sqrt 7$ that would be acceptable.
$endgroup$
– Deepak
Dec 2 '18 at 3:16
$begingroup$
@martha Do you mean to convert any rational number?
$endgroup$
– Toby Mak
Dec 2 '18 at 3:41
$begingroup$
@martha Do you mean to convert any rational number?
$endgroup$
– Toby Mak
Dec 2 '18 at 3:41
2
2
$begingroup$
If $r=sqrt a+sqrt b$, then $rgesqrt a$, so $ale r^2$, and similarly $ble r^2$. So if worst comes to worst you can just check every pair $(a,b)$ up to $r^2$ to see which one comes closest. Not quite as bad as it sounds, as for each value of $a$ that you try, you can compute $(r-sqrt a)^2$ to see what value of $b$ to try.
$endgroup$
– Gerry Myerson
Dec 2 '18 at 3:48
$begingroup$
If $r=sqrt a+sqrt b$, then $rgesqrt a$, so $ale r^2$, and similarly $ble r^2$. So if worst comes to worst you can just check every pair $(a,b)$ up to $r^2$ to see which one comes closest. Not quite as bad as it sounds, as for each value of $a$ that you try, you can compute $(r-sqrt a)^2$ to see what value of $b$ to try.
$endgroup$
– Gerry Myerson
Dec 2 '18 at 3:48
add a comment |
0
active
oldest
votes
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
});
}
});
draft saved
draft discarded
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%2f3022179%2fhow-to-convert-any-decimal-number-in-form-of-sqrt-a-sqrt-b%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3022179%2fhow-to-convert-any-decimal-number-in-form-of-sqrt-a-sqrt-b%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
1
$begingroup$
$4.88 neq sqrt 5 + sqrt 7$ LHS is rational, RHS is irrational. If you'd written $4.88 approx sqrt 5 + sqrt 7$ that would be acceptable.
$endgroup$
– Deepak
Dec 2 '18 at 3:16
$begingroup$
@martha Do you mean to convert any rational number?
$endgroup$
– Toby Mak
Dec 2 '18 at 3:41
2
$begingroup$
If $r=sqrt a+sqrt b$, then $rgesqrt a$, so $ale r^2$, and similarly $ble r^2$. So if worst comes to worst you can just check every pair $(a,b)$ up to $r^2$ to see which one comes closest. Not quite as bad as it sounds, as for each value of $a$ that you try, you can compute $(r-sqrt a)^2$ to see what value of $b$ to try.
$endgroup$
– Gerry Myerson
Dec 2 '18 at 3:48