Math, asked by hijabzahra0, 11 months ago

can someone help me with this?

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Answered by shivisharma

hope it helps you .
Please mark me brainliest

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poojayadav00: it is wrong.....

poojayadav00: i hav solved but now it cant anwer it....

hijabzahra0: Yeah it's wrong.. can u tell the way u have done pooja yadav?

hijabzahra0: shivi sharma, thanks anyway :)) glad that u took time to help me..

shivisharma: ok if my answer is wrong so pooja yadav you answer this question

hijabzahra0: your mistake is this that root 3 square is never 9 and root 5 square is never 25.. peace! I am also waiting for her to reply so that I can get the answer as well..

poojayadav00: i cant send any picture here but first u solve the square so u will get (8+√15) then prove that √15 is irrational,as the sum of any irrational or rational number is always iraational so we will conclude that 8+√15 is also irrational.....

poojayadav00: (√3+√5)²
3+5+√15
8+√15

Let √15 be rational number in the form of p/q
where p and q are co primes i.e they hav only 1 as a common factor and q is not equal to zero...
So,√15=p/q
15=p²/q²
15q²=p²
Since 15 divides p² so it divides p also...
Now let
p=15c for some integer c
Then 15=(15c)²/q²
15=225c²/q²
15c²=q²
Since 15 divides q² so it divides q also...

poojayadav00: But this is contradiction to the fact that p and q dont have any common factor rather 1
Hence p and q dont have any other common factor...so √15 is irrational.

Now let (8+√15) also be a rational number 17 in the form of t/s where t and s are coprimes and s is not equal to zero...
8+√15=t/s
√15=t/s-8
√15=t-8s/t
As t,s and 8 are rational numbers or natural numbers so (t-8s/3) is also a rational nuber but this contadicts the fact that √15 is irrational....

poojayadav00: Hence our assumption is wrong hence 8+√15[ (√3+√5)² ] is irrational...

Hope this helps u....

Answered by poojayadav00

(√3+√5)²
3+5+√15
8+√15

Let √15 be rational number in the form of p/q
where p and q are co primes i.e they hav only 1 as a common factor and q is not equal to zero...
So,√15=p/q
15=p²/q²
15q²=p²
Since 15 divides p² so it divides p also...
Now let
p=15c for some integer c
Then 15=(15c)²/q²
15=225c²/q²
15c²=q²
Since 15 divides q² so it divides q also...
But this is contradiction to the fact that p and q dont have any common factor rather 1
Hence p and q dont have any other common factor...so √15 is irrational.

Now let (8+√15) also be a rational number 17 in the form of t/s where t and s are coprimes and s is not equal to zero...
8+√15=t/s
√15=t/s-8
√15=t-8s/t
As t,s and 8 are rational numbers or natural numbers so (t-8s/3) is also a rational nuber but this contadicts the fact that √15 is irrational....
Hence our assumption is wrong hence 8+√15[ (√3+√5)² ] is irrational...

Hope this helps u....

hijabzahra0: thank you pooja. it helped a lot!

poojayadav00: :)

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