prove that 7+2√3 is an irrational number
Answers
Step-by-step explanation:
Let assume that 7-2root3 be rational and rational numbers are in the form of p/q form.
\begin{gathered}7 - 2 \sqrt{3} = \frac{p}{q} \\ 7 - \frac{p}{q} = 2 \sqrt{3} \\ \frac{7q - p}{q} = 2 \sqrt{3} \\ \frac{7q - p}{2q} = \sqrt{3} \end{gathered}
7−2
3
=
q
p
7−
q
p
=2
3
q
7q−p
=2
3
2q
7q−p
=
3
We know that root 3 is irrational and not p/q form. It contradicts the statement that it is irrational as it is p/q form.
Subtraction and multiplication of irrational number form irrational number so
7-2root3 is irrational.
Answer: = 7+2 = 9 ,
= 9 * √3 cannot be made in to standard form So ,
It is a irrational number AS A RATIONAL NUMBER MUST BE IN THE FORM OF p/q WHERE q ≠0 . And this problem cannot be written like that .
Step-by-step explanation: Please mark me as the brainliest .