UPSC Exam > UPSC Questions > Rationalise the denominator and find the valu...
Start Learning for Free
Rationalise the denominator and find the value of (7−√3)/ (7+√3)?
Most Upvoted Answer
Rationalise the denominator and find the value of (7−√3)/ (7+√3)?
Expressing the given expression in a simpler form:
To rationalize the denominator of the expression \(\frac{7 - \sqrt{3}}{7 + \sqrt{3}}\), we need to multiply both the numerator and the denominator by the conjugate of the denominator, which is \(7 - \sqrt{3}\).
Rationalizing the denominator:
\[\frac{7 - \sqrt{3}}{7 + \sqrt{3}} \times \frac{7 - \sqrt{3}}{7 - \sqrt{3}}\]
\[= \frac{(7 - \sqrt{3})(7 - \sqrt{3})}{(7 + \sqrt{3})(7 - \sqrt{3})}\]
\[= \frac{49 - 14\sqrt{3} + 3}{49 - 3}\]
\[= \frac{52 - 14\sqrt{3}}{46}\]
Final simplified expression:
Therefore, the simplified form of \(\frac{7 - \sqrt{3}}{7 + \sqrt{3}}\) after rationalizing the denominator is \(\frac{52 - 14\sqrt{3}}{46}\).
To rationalize the denominator of the expression \(\frac{7 - \sqrt{3}}{7 + \sqrt{3}}\), we need to multiply both the numerator and the denominator by the conjugate of the denominator, which is \(7 - \sqrt{3}\).
Rationalizing the denominator:
\[\frac{7 - \sqrt{3}}{7 + \sqrt{3}} \times \frac{7 - \sqrt{3}}{7 - \sqrt{3}}\]
\[= \frac{(7 - \sqrt{3})(7 - \sqrt{3})}{(7 + \sqrt{3})(7 - \sqrt{3})}\]
\[= \frac{49 - 14\sqrt{3} + 3}{49 - 3}\]
\[= \frac{52 - 14\sqrt{3}}{46}\]
Final simplified expression:
Therefore, the simplified form of \(\frac{7 - \sqrt{3}}{7 + \sqrt{3}}\) after rationalizing the denominator is \(\frac{52 - 14\sqrt{3}}{46}\).
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Rationalise the denominator and find the value of (7−√3)/ (7+√3)?
Question Description
Rationalise the denominator and find the value of (7−√3)/ (7+√3)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Rationalise the denominator and find the value of (7−√3)/ (7+√3)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rationalise the denominator and find the value of (7−√3)/ (7+√3)?.
Rationalise the denominator and find the value of (7−√3)/ (7+√3)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Rationalise the denominator and find the value of (7−√3)/ (7+√3)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rationalise the denominator and find the value of (7−√3)/ (7+√3)?.
Solutions for Rationalise the denominator and find the value of (7−√3)/ (7+√3)? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Rationalise the denominator and find the value of (7−√3)/ (7+√3)? defined & explained in the simplest way possible. Besides giving the explanation of
Rationalise the denominator and find the value of (7−√3)/ (7+√3)?, a detailed solution for Rationalise the denominator and find the value of (7−√3)/ (7+√3)? has been provided alongside types of Rationalise the denominator and find the value of (7−√3)/ (7+√3)? theory, EduRev gives you an
ample number of questions to practice Rationalise the denominator and find the value of (7−√3)/ (7+√3)? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup