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Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2?
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Rationalize the denominator of each of the following 1 + root 2 upon 2...
Rationalizing the Denominator of 1 + √2 / 2 - √2
To rationalize the denominator of the expression 1 + √2 / 2 - √2, we need to eliminate the radical from the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
Step 1: Identify the Conjugate
The conjugate of 2 - √2 is 2 + √2.
Step 2: Multiply Numerator and Denominator by the Conjugate
(1 + √2) * (2 + √2) / (2 - √2) * (2 + √2)
Step 3: Simplify the Expression
Numerator: (1 * 2) + (1 * √2) + (√2 * 2) + (√2 * √2) = 2 + √2 + 2√2 + 2
= 4 + 3√2
Denominator: (2 * 2) + (2 * √2) - (√2 * 2) - (√2 * √2) = 4
= 4
Step 4: Final Answer
The rationalized form of 1 + √2 / 2 - √2 is (4 + 3√2) / 4.
To rationalize the denominator of the expression 1 + √2 / 2 - √2, we need to eliminate the radical from the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
Step 1: Identify the Conjugate
The conjugate of 2 - √2 is 2 + √2.
Step 2: Multiply Numerator and Denominator by the Conjugate
(1 + √2) * (2 + √2) / (2 - √2) * (2 + √2)
Step 3: Simplify the Expression
Numerator: (1 * 2) + (1 * √2) + (√2 * 2) + (√2 * √2) = 2 + √2 + 2√2 + 2
= 4 + 3√2
Denominator: (2 * 2) + (2 * √2) - (√2 * 2) - (√2 * √2) = 4
= 4
Step 4: Final Answer
The rationalized form of 1 + √2 / 2 - √2 is (4 + 3√2) / 4.
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Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2?
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Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2?.
Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rationalize the denominator of each of the following 1 + root 2 upon 2 - root 2?.
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