Question

show that 3÷2√5 is a irrational no.​

Answer 1

Answer:

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Answer 2

FIRSTLY THANKS FOR OPPURTUNITY

@₦S₩ER H₤R₤ ....

LET 3÷2√5 A IRRATIONAL NO.

SO, 3/2√5=R(R IS A RATIONAL NO.) -(A)

√5=3R/2

√5=P/Q (P AND Q ARE CO-PRIME AND QNOT EQUAL TO 0)

SQUARING BOTH SIDE

5=P²/Q²

5 DIVIDES P^2

SO, 5 DIVIDES P

5Q^2=(5M)^2 (FOR SOME M )

5Q^2=25M^2

Q^2=5M^2

5 DIVIDES Q^2

5 DIVIDES Q

*IT MEANS 5 DIVIDES BOTH P AND Q

BUT IT IS A CONTRADICTION AS P AND Q ARE CO-PRIMES

SO, LHS OF (A)  IS A IRRATIONAL NO.

SO, RHS OF (A) MUST BE IRRATIONAL

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