p.t 2√3+√5 is irrational
Answers
Answered by
1
Step-by-step explanation:
Let us assume that 2
3
+
5
is rational number.
Let P=2
3
+
5
is rational
on squaring both sides we get
P
2
=(2
3
+
5
)
2
=(2
3
)
2
+(
5
)
2
+2×2
3
×
5
P
2
=12+5+4
15
P
2
=17+4
15
4
P
2
−17
=
15
………..(1)
Since P is rational no. therefore P
2
is also rational &
4
P
2
−17
is also rational.
But
15
is irrational & in equation(1)
4
P
2
−17
=
15
Rational
= irrational
Hence our assumption is incorrect & 2
3
+
5
is irrational number.
Answered by
1
Answer:
This shows (a-3b)/2b is a rational number. But we know that √5 is an irrational number. So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect
Similar questions