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Prove that route 5 is irrational

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Prove that route 5 is irrational

    • Posted by Dalvi Sir 6 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 6 answers

    Kavya Khurana 6 years, 5 months ago

    Hence, ROOT 5 is irrational ??????

    0Thank You

    Sejal Kathait?????? 6 years, 5 months ago

    Let√ 2 be a rational number Therefore,√2 =a/b Where a & b are Co-prime integers &b is not = 0 Therefore,a/b=√2 a= √2b Squaring both sides (a)2=(√2b)2 a2= 2b2......(1) This implies 2 divides a2 So,2 ➗ a So let a = 2 c for some integer Put this in (1...) (2c)2 = 2b square 4c square= 2b square 2c square= b square This implies, 2 divides b square So,2 divides b Therefor, a & have 2 as commen factor but this contradicts that a & b no common factor then b. Therefore our aaaumption is wrong Hence √2 is irrational This is the method of doing question you just have to change it from √ 2 to √5 and all over method is same..

    0Thank You

    Yogita Ingle 6 years, 5 months ago

    Let us assume that √5 is a rational number.
    we know that the rational numbers are in the form of p/q form where p,q are integers.
    so, √5 = p/q
         p = √5q
    we know that 'p' is a rational number. so √5 q must be rational since it equals to p
    but it doesn't occurs with √5 since its not an integer
    therefore, p = √5q
    this contradicts the fact that √5 is an irrational number
    hence our assumption is wrong and √5 is an irrational number.

     

    1Thank You

    Sejal Kathait?????? 6 years, 5 months ago

    This app is for aking homework related questions. And he is doing ✔

    0Thank You

    Rohit Sharma 6 years, 5 months ago

    This app is for chatting olny

    1Thank You

    Rohit Sharma 6 years, 5 months ago

    Ask to your teacher don't ask this type of questions in this app

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