Question

Show that 3+7√2 is an irrational number . Is the sum of two irrational numbers always irrational number ?

Answer 1

Yes the sum of two irrational numbers is always irrational.

Answer 2

Answer:

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10th

Maths

Real Numbers

Revisiting Irrational Numbers

Prove that √(2) + √(3) is ...

MATHS

Prove that

2

+

3

is an irrational number.

EASY

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ANSWER

First we prove that

2

is irrational.

for that we assume that

2

is rational. And as rational number can be written as

q

p

form.

where we assume that p and q have no common factor. Squaring in both side. After that

2=

q

2

p

2

which implies that

p

2

=2q

2

thus p

2

is even. The only way this can be true is that p itself is even. But then p

2

is actually divisible by 4. Hence q

2

and therefore q must be even. So p and q are both even which is a contradiction to our assumption that they have no common factors. The square root of 2 cannot be rational.

and we similarly prove for

3

.

And as we know that sum of two irrational no. is always irrational.