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Simplify the following by rationalising 6-4√3/6+4√3?
Most Upvoted Answer
Simplify the following by rationalising 6-4√3/6+4√3?
Step-by-step Explanation:
Given expression:
6 - 4√3 / 6 + 4√3
Rationalizing the denominator:
To simplify the given expression, we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
Conjugate of the denominator:
The conjugate of 6 + 4√3 is 6 - 4√3.
Multiplying the numerator and denominator by the conjugate:
((6 - 4√3) / (6 + 4√3)) * ((6 - 4√3) / (6 - 4√3))
= (36 - 24√3 - 24√3 + 48) / (36 - 24√3 + 24√3 - 48)
= (84 - 48√3) / (36 - 48)
= (84 - 48√3) / (-12)
= -7 + 4√3
Therefore, the simplified form of the given expression is -7 + 4√3.
Given expression:
6 - 4√3 / 6 + 4√3
Rationalizing the denominator:
To simplify the given expression, we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
Conjugate of the denominator:
The conjugate of 6 + 4√3 is 6 - 4√3.
Multiplying the numerator and denominator by the conjugate:
((6 - 4√3) / (6 + 4√3)) * ((6 - 4√3) / (6 - 4√3))
= (36 - 24√3 - 24√3 + 48) / (36 - 24√3 + 24√3 - 48)
= (84 - 48√3) / (36 - 48)
= (84 - 48√3) / (-12)
= -7 + 4√3
Therefore, the simplified form of the given expression is -7 + 4√3.
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Simplify the following by rationalising 6-4√3/6+4√3?
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Simplify the following by rationalising 6-4√3/6+4√3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Simplify the following by rationalising 6-4√3/6+4√3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify the following by rationalising 6-4√3/6+4√3?.
Simplify the following by rationalising 6-4√3/6+4√3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Simplify the following by rationalising 6-4√3/6+4√3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify the following by rationalising 6-4√3/6+4√3?.
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