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In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2
rational numbers between P and Q.?
rational numbers between P and Q.?
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In the following picture OA=OB=1unit. Identify the irrational numbers ...
Identifying Irrational Numbers P and Q
- Given that OA=OB=1 unit, we can see that the line segment AB is the hypotenuse of a right triangle with legs of length 1 unit each.
- Using the Pythagorean theorem, we can calculate the length of AB:
AB^2 = OA^2 + OB^2
AB^2 = 1^2 + 1^2
AB^2 = 2
AB = √2
- Therefore, the length of the line segment AB is √2. Since √2 is not a rational number (cannot be expressed as a fraction of two integers), it is an irrational number. So, P = Q = √2.
Identifying Rational Numbers between P and Q
- To find two rational numbers between P and Q, we can use the concept of decimal expansions.
- The decimal expansion of √2 is non-terminating and non-repeating, while rational numbers have decimal expansions that are either terminating or repeating.
- We can approximate √2 as 1.4 and 1.5, which are rational numbers.
- Two rational numbers between 1.4 and 1.5 could be 1.41 and 1.42. These numbers are rational and lie between P and Q (√2).
Therefore, the irrational numbers P and Q are √2, and two rational numbers between them are 1.41 and 1.42.
- Given that OA=OB=1 unit, we can see that the line segment AB is the hypotenuse of a right triangle with legs of length 1 unit each.
- Using the Pythagorean theorem, we can calculate the length of AB:
AB^2 = OA^2 + OB^2
AB^2 = 1^2 + 1^2
AB^2 = 2
AB = √2
- Therefore, the length of the line segment AB is √2. Since √2 is not a rational number (cannot be expressed as a fraction of two integers), it is an irrational number. So, P = Q = √2.
Identifying Rational Numbers between P and Q
- To find two rational numbers between P and Q, we can use the concept of decimal expansions.
- The decimal expansion of √2 is non-terminating and non-repeating, while rational numbers have decimal expansions that are either terminating or repeating.
- We can approximate √2 as 1.4 and 1.5, which are rational numbers.
- Two rational numbers between 1.4 and 1.5 could be 1.41 and 1.42. These numbers are rational and lie between P and Q (√2).
Therefore, the irrational numbers P and Q are √2, and two rational numbers between them are 1.41 and 1.42.
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In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2 rational numbers between P and Q.?
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In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2 rational numbers between P and Q.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2 rational numbers between P and Q.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2 rational numbers between P and Q.?.
In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2 rational numbers between P and Q.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2 rational numbers between P and Q.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following picture OA=OB=1unit. Identify the irrational numbers P and Q. Also write 2 rational numbers between P and Q.?.
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