sum of irrational number & rational number needn't be a irrational number.
Asked by Ayan | 28th Jul, 2014, 03:51: PM
Expert Answer:
No, sum of irrational number and rational number is always irrational.
Let x be irrational and r be rational.
Assume that x + r = t is rational. Then x = t - r is the difference of two rational numbers and therefore rational. However this contradicts the assumption that x is irrational.
Therefore x + r is irrational
Assume that x + r = t is rational. Then x = t - r is the difference of two rational numbers and therefore rational. However this contradicts the assumption that x is irrational.
Therefore x + r is irrational
Answered by Dharma Teja | 28th Jul, 2014, 06:42: PM
Application Videos
Concept Videos
- what is meant by irrational number
- Rationalise the denominator of the following 1/√7-√6
- find value of a and b if
7+^5/7-^5 - 7-^5/7+^5= a+7^5b/11
- (5+√3)(6+√5)
- show how √5 can be represented on the number line
- if √2=1.414,then the value of √3+√6 up to 3 places of decimal is _
- what is irrational
- 2-root5 is it rational or irrational? and how?
- Are the square root of all positive integers irrational ?if not give an example of the square root of a rational number that is a ra
- how to add roots l
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Sign Up
Verify mobile number
Enter the OTP sent to your number
Change