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The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)
(a) 20
(b) 2
(c) 5?
(a) 20
(b) 2
(c) 5?
Most Upvoted Answer
The smallest irrational number by which √20 should be multipled so as ...
The smallest irrational number to multiply with √20 to yield a rational number can be determined by analyzing the factors involved.
Understanding √20
- √20 can be simplified as √(4 × 5).
- This simplifies to 2√5.
- The term √5 is irrational, which is crucial in our calculations.
Finding the Required Multiplier
- To convert an irrational number into a rational one, we need to eliminate the square root.
- Multiplying √20 (or 2√5) by √5 will help us achieve this.
Calculation
- If we multiply 2√5 by √5:
(2√5) × (√5) = 2 × (√5 × √5) = 2 × 5 = 10.
- The result, 10, is a rational number.
Identifying the Smallest Irrational Number
- We note that the smallest irrational number we used for this multiplication was √5.
- Therefore, √5 is the required irrational number that, when multiplied with √20, results in a rational number.
Conclusion
- Among the options given: (a) 20, (b) 2, (c) 5, none correspond to √5 directly.
- However, since none of the options match, the answer remains √5 as the smallest irrational number needed.
Thus, the smallest irrational number to multiply with √20 to achieve a rational result is **√5**.
Understanding √20
- √20 can be simplified as √(4 × 5).
- This simplifies to 2√5.
- The term √5 is irrational, which is crucial in our calculations.
Finding the Required Multiplier
- To convert an irrational number into a rational one, we need to eliminate the square root.
- Multiplying √20 (or 2√5) by √5 will help us achieve this.
Calculation
- If we multiply 2√5 by √5:
(2√5) × (√5) = 2 × (√5 × √5) = 2 × 5 = 10.
- The result, 10, is a rational number.
Identifying the Smallest Irrational Number
- We note that the smallest irrational number we used for this multiplication was √5.
- Therefore, √5 is the required irrational number that, when multiplied with √20, results in a rational number.
Conclusion
- Among the options given: (a) 20, (b) 2, (c) 5, none correspond to √5 directly.
- However, since none of the options match, the answer remains √5 as the smallest irrational number needed.
Thus, the smallest irrational number to multiply with √20 to achieve a rational result is **√5**.
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The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)(a) 20(b) 2(c) 5?
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The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)(a) 20(b) 2(c) 5? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)(a) 20(b) 2(c) 5? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)(a) 20(b) 2(c) 5?.
The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)(a) 20(b) 2(c) 5? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)(a) 20(b) 2(c) 5? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024)(a) 20(b) 2(c) 5?.
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