(2+root2)(2-root2) is rational or irrational if you don't know please don't answer others wise i will report the answer it's very important
Share
(2+root2)(2-root2) is rational or irrational if you don't know please don't answer others wise i will report the answer it's very important
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
hi how are you i try my best
Now, we know that √2 is an irrational number, hence 4√2 is also an irrational number. Therefore, √32 is an irrational number.
...
Prove that Root 2 is Irrational Number.
1. Prove that Root 2 is Irrational Number
2. Prove That Root 2 is Irrational by Contradiction Method
3. Prove That Root 2 is Irrational by Long Division Method
stay bless stay safe stay happy stay healthy and be your self
Step-by-step explanation:
Answer:
Solution:
Let us suppose that √2+√3 is rational.
Let √2+√3=\frac{a}{b}
b
a
,
where a,b are integers and b≠0
Therefore,
\sqrt{2}=\frac{a}{b}-\sqrt{3}
2
=
b
a
−
3
On Squaring both sides , we get
2=\frac{a^{2}}{b^{2}}+3-2\times\frac{a}{b}\times\sqrt{3}2=
b
2
a
2
+3−2×
b
a
×
3
Rearranging the terms ,
\frac{2a}{b}\times\sqrt{3}=\frac{a^{2}}{b^{2}}+3-2
b
2a
×
3
=
b
2
a
2
+3−2
= \frac{a^{2}}{b^{2}}+1=
b
2
a
2
+1
\sqrt{3}=\frac{a^{2}+b^{2}}{2ab}
3
=
2ab
a
2
+b
2
Since , a,b are integers ,
\frac{a^{2}+b^{2}}{2ab}
2ab
a
2
+b
2
is rational, and so √3 is rational.
This contradicts the fact √3 is irrational.
Hence, √2+√3 is irrational.
•••••