Yes. Consider 4+sqrt(2), and 3-sqrt(2). Both are irrational numbers. Their sum is 7.
Yes, you can.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
Find the difference between the two numbers, then add an irrational number between zero and one, divided by this difference, to the lower number. Such an irrational number might be pi/10, (square root of 2) / 2, etc.
Sometimes. eg the irrational number √2 squared is 2 which is rational (2 = 2/1) eg the irrational number √(√2) squared is √2 which is irrational.
Yes. sqrt(2) + sqrt(2) = 2*sqrt(2), an irrational number.
You can add any irrational number.
No, but you can add an irrational number and a rational number to give an irrational.For example, 1 + pi is irrational.
An irrational number.
Every time. No exceptions.
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
Yes. Consider 4+sqrt(2), and 3-sqrt(2). Both are irrational numbers. Their sum is 7.
Yes, you can.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
Find the difference between the two numbers, then add an irrational number between zero and one, divided by this difference, to the lower number. Such an irrational number might be pi/10, (square root of 2) / 2, etc.
Sometimes. eg the irrational number √2 squared is 2 which is rational (2 = 2/1) eg the irrational number √(√2) squared is √2 which is irrational.
Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.