Question

be quick please

quick​

Answer 1

YO DUDE

LET 3 ROOT 2 BE A RATIONAL NUMBER

3 ROOT 2=P/Q

ROOT 2=P/3Q

FROM EQUATION 1 WE CAN CONCLUDE THAT P/3Q ARE INTEGERS BUT ROOT 2 IS NOT AN INTEGER

SO OUR SUPPOSITION IS WRONG

HENCE 3 ROOT 2 IS AN IRRATIONAL NUMBER

PLS MARK BRAINLIEST BRO

Answer 2

Solution:-

To Proof:-

• ³√2 is an Irrational Number.

Proof:-

Let ³√2 be an Rational Number.

=) ³√2 can be written as p/q where q ≠ 0 and p and q are co-prime Numbers.

=) ³√2 = p/q

Cubing on both the sides.

=) ( ³√2)³ = (p/q)³

=) 2 = p³/q³

=) 2q³ = p³

Here,

2 divides p³. so it will also divide p_____(1)

Taking [ p = 2a ].

=) 2q³ = ( 2a)³

=) 2q³ = 8a³

=) q³ = 4a³

Here,

2 divides q³ . So it will also divide q ____(2)

From eq(1) and eq(2). we get

2 divides p as well as q which Contradicts that p and q are co-prime Numbers.

Hence,

³√2 is an Irrational Number.