Question

5. Show that:
(i) Negative of an irrational number is irrational
(ii) The product of a non-zero rational number and an irrational number is an irrational number.​

Answer 1

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ᎽᎾUℛ. ᎯℕЅᏇℰℛ ℐЅ ℋℰℛℰ ࿓⚕

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$answer \: \: 1) = >$
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Let negative of an irrational be rational number 
let P be an irrational number therefore by the assumption -p is  a rational number 
since negative of a rational number is rational.-(-P)= P
is  a rational number   but we assumed P as an irrational number ... so our assumption is wrong  so negative of an irrational number is irrational ......

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$answer \: \: 2) = >$
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on zero rational numbers are 1,2,3,4,5......

Irrational numbers are √2,√3,√5,√6......

Product of non zero rational number with irrational number.

1×√2 = √2

2×√2 = 2√2

4×√3 = 4√3

All results are irrational numbers.

Therefore,the product of a non zero rational number with an irrational number is always irrational.

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Answer 2

HEY BUDDY....HERE'S YOUR ANSWER...

(i)Let a be an irrational number,

So negative of the irrational number is irrational.

a= -a

Example:- _/3= -_/3

(ii)Example:-

Non zero rational number=a= 1/2

Irrational number=b=_/2

So,a×b=1/2×_/2

=_/2/2

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