Q. 14.3( 21 Votes )
Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.
Given: x is rational number and y is irrational number.
Yes, x + y is necessarily an irrational number.
Example: Let x = 2, which is rational.
Let y = √2, which is irrational.
Then, x + y = 2 + √2, which is irrational.
∴ Sum of a rational and an irrational number is always irrational.
Rate this question :
If x is rational and y is irrational, then show that (x + y) is always irrational.RS Aggarwal & V Aggarwal - Mathematics
If =1.414, then the value of upto three place of decimal isRD Sharma - Mathematics
If =1.4142, then is equal toRD Sharma - Mathematics
The value of isRD Sharma - Mathematics
If x = , then x2 + -2 =RD Sharma - Mathematics
If , then a =RD Sharma - Mathematics
If x = 3+, find the value of x2+.RD Sharma - Mathematics
The decimal representation of an irrational number isRS Aggarwal & V Aggarwal - Mathematics
Write four irrational numbers between 0.1 and 0.2.RS Aggarwal & V Aggarwal - Mathematics