Question

prove that the following numbers are irrational.

Answer 1

Your answer is here

14)
(I) 5+√2

Let us assume √2 is a rational
√2=p/q(where p and q are co-prime)

squaring on both the sides
(√2)^2=p^2/q^2
2=p^2/q^2
2q^2=p^2
q^2=p^2/2
√2 divides p^2 and p also

Let P=2m
2q^2=(2m)^2
2q^2=4m^2
m^2=2q^2/4
m^2=q^2/2
√2 divides q^2 and q also

It is contradiction
Our assumption is wrong
Hence, √2 is irrational
5+√2 is irrational because the sum of rational and irrational is irrational.
Hence PROVED………

ANOTHER TWO PROBLEMS ARE SAME METHOD BUT SIGNS ARE DIFFERENT

HOPE IT HELPS ………

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Answer 2

Answer:

Step-by-step explanation:

5+✓2 is irrational number.

Let us assume 5+✓2 is rational

5+✓2=a/b

(Where a,b are co-integers and b is not = to 0)

5+✓2=a/b

✓2=a/b-5

✓2=a/b-5/1

✓2=a-5b/b

This contradicts that 5+✓2 is irrational.

But our assumption is wrong.

Therefore,5+✓2 is an irrational number.

Hope this helps you guys

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