Plz do 1and 5 bit ,do it plz i have to submit it tomorrow plz help
Answers
Step-by-step explanation:
(ii) √3+√5
= as,√3 nd √5 are irrational number . therefore, it is also a irrational.
(v) 3+2√5
= it is also a irrational no. as 2√5 is a irrational number.
hope this helped u
Answer:
We will prove it by the method of contradiction.
Let 1/√2 is a rational number
So we can write 1/√2 = a/b .........1
where a and b are relatively prime numbers.
Squaring equation 1 on bothe side,
(1/√2)2 = (a/b)2
=> 1/2 = a2 /b2
=> 2a2 = b2
So b2 is an even number
=> b must be an even number
Let b = 2c
On squaring both side,
=> b2 = (2c)2
=> b2 = 4c2
now from equation 1
2a2 = 4c2
=> a2 = 2c2
=> a must be an even number.
Now since both a and b are even numbers, then a and b can not be relatively prime.
So our assumption is wrong.
Hense 1/√2 is an irrational number.
Hope it helps
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