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√5 is irriational |
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Answer» Yes it is irrational 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 intezers.so, √5 = p/q p = √5qwe know that \'p\' is a rational number. so √5 q must be rational since it equals to pbut it doesnt occurs with √5 since its not an intezertherefore, p =/= √5qthis contradicts the fact that √5 is an irrational numberhence our assumption is wrong and √5 is an irrational number.\xa0 Yes Therefore, it can be written in the form of p/q. √5=p/q........ equation 1On squaring both sides(√5)^2=[p/q]^25=p^2/q^2q^2=p^2/5. ..............2Clearly, p is divisible by 5Now put q=5a in equation 2 Therefore, 25a^2=5p^2Therefore,. q is also divisible by 5 Our assumption was wrong √5 is an irrational no. Hence, proved Let √5 be a rational no. |
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