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Which of the following is irrational?
- a)Product of (3 - √27) and (√9 + 3√3)
- b)Sum of (5 - 4√2) and 4(6 + √2)
- c)Sum of √4761 and √5175
- d)Product of √16875 and √27
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Which of the following is irrational?a)Product of (3 - √27) and (√9 +...
Product of (3 - √27) and (√9 + 3√3)
= (3 - 3√3)(3 + 3√3)
= - 18 (which is not irrational)
Option (2):
= Sum of (5 - 4√2) and 4(6 + √2)
= (5 - 4√2) + 4(6 + √2)
= 5 - 4√2 + 24 + 4√2
= 29 (which is not irrational)
Option (3):
= Sum of √4761 and √5175
= 69 + 15√23 (which is irrational)
Option (4):
= Product of √16875 and √27
= 75√3 x 3√3
= 675 (which is not irrational)
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Which of the following is irrational?a)Product of (3 - √27) and (√9 +...
Understanding the Problem
To determine which option is irrational, we need to analyze each expression carefully. An irrational number cannot be expressed as a simple fraction, while a rational number can.
Option A: Product of (3 - √27) and (√9 + 3√3)
- Calculate √27 = 3√3
- Thus, 3 - √27 = 3 - 3√3 (this is irrational)
- √9 = 3, so √9 + 3√3 = 3 + 3√3 (this is also irrational)
- The product of two irrational numbers can be either rational or irrational; hence, we cannot conclude yet.
Option B: Sum of (5 - 4√2) and 4(6 + √2)
- Simplify: 4(6 + √2) = 24 + 4√2
- Now, (5 - 4√2) + (24 + 4√2) = 29 (this is rational)
Option C: Sum of √4761 and √5175
- Calculate √4761 = 69 (since 69 * 69 = 4761, it's rational)
- Calculate √5175 = √(25 * 207) = 5√207 (√207 is irrational)
- Therefore, 69 + 5√207 is irrational, as the sum of a rational and an irrational number is irrational.
Option D: Product of √16875 and √27
- √16875 = √(25 * 675) = 5√675, which is rational.
- √27 = 3√3, which is also irrational.
- The product of an irrational number and a rational number can be irrational, but we need to verify further.
Conclusion
The only option that yields an irrational result is Option C, where the sum of a rational number and an irrational number produces an irrational number.
To determine which option is irrational, we need to analyze each expression carefully. An irrational number cannot be expressed as a simple fraction, while a rational number can.
Option A: Product of (3 - √27) and (√9 + 3√3)
- Calculate √27 = 3√3
- Thus, 3 - √27 = 3 - 3√3 (this is irrational)
- √9 = 3, so √9 + 3√3 = 3 + 3√3 (this is also irrational)
- The product of two irrational numbers can be either rational or irrational; hence, we cannot conclude yet.
Option B: Sum of (5 - 4√2) and 4(6 + √2)
- Simplify: 4(6 + √2) = 24 + 4√2
- Now, (5 - 4√2) + (24 + 4√2) = 29 (this is rational)
Option C: Sum of √4761 and √5175
- Calculate √4761 = 69 (since 69 * 69 = 4761, it's rational)
- Calculate √5175 = √(25 * 207) = 5√207 (√207 is irrational)
- Therefore, 69 + 5√207 is irrational, as the sum of a rational and an irrational number is irrational.
Option D: Product of √16875 and √27
- √16875 = √(25 * 675) = 5√675, which is rational.
- √27 = 3√3, which is also irrational.
- The product of an irrational number and a rational number can be irrational, but we need to verify further.
Conclusion
The only option that yields an irrational result is Option C, where the sum of a rational number and an irrational number produces an irrational number.
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Which of the following is irrational?a)Product of (3 - √27) and (√9 + 3√3)b)Sum of (5 - 4√2) and 4(6 + √2)c)Sum of √4761 and √5175d)Product of √16875 and √27Correct answer is option 'C'. Can you explain this answer? for Railways 2026 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Which of the following is irrational?a)Product of (3 - √27) and (√9 + 3√3)b)Sum of (5 - 4√2) and 4(6 + √2)c)Sum of √4761 and √5175d)Product of √16875 and √27Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is irrational?a)Product of (3 - √27) and (√9 + 3√3)b)Sum of (5 - 4√2) and 4(6 + √2)c)Sum of √4761 and √5175d)Product of √16875 and √27Correct answer is option 'C'. Can you explain this answer?.
Which of the following is irrational?a)Product of (3 - √27) and (√9 + 3√3)b)Sum of (5 - 4√2) and 4(6 + √2)c)Sum of √4761 and √5175d)Product of √16875 and √27Correct answer is option 'C'. Can you explain this answer? for Railways 2026 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Which of the following is irrational?a)Product of (3 - √27) and (√9 + 3√3)b)Sum of (5 - 4√2) and 4(6 + √2)c)Sum of √4761 and √5175d)Product of √16875 and √27Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is irrational?a)Product of (3 - √27) and (√9 + 3√3)b)Sum of (5 - 4√2) and 4(6 + √2)c)Sum of √4761 and √5175d)Product of √16875 and √27Correct answer is option 'C'. Can you explain this answer?.
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