Prove that √5 is irrational hense show that 3+ 2√5 is irrational
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Answer:
ROOT 5 PROVED AS IRRATIONAL
Step-by-step explanation:
LET ROOT 5 BE A RATIONAL NUMBER . THEREFORE WE CAN FIND INTEGER A AND B (WHERE B IS NOT EQUAL TO 0 )AND A AND B ARE CO PRIME ) SUCH THAT A/B=ROOT 5 .
=A=ROOT 5.B
SQUARING BOTH SIDE WE HAVE ASQ=5BSQ.
THEREFOR 5 DIVIDES A SQ =5DIVIDES A .
a=5c,where c is integer .
putting a=1 .we have
5c=root 5c.=5bsq
=25csq=5bsq
=5csq=bsq.
5 divided by sq =5 divides b .
from (1) and (2) .
there fore our supposition that root 5 is rational Is wrong .
HOPE IT HELPED !2
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