Question

Show that√5 is not a rational number

Answer 1

Answer:

$\begin{array}{c|cc}2&5.00\ 00\ 00\ 00\ 00}\ 00\ 00\ 00\ 00\\ \underline{\ \ \ 2\ \ \ }&\underline{-4 \qquad\ \ }\qquad\ \ \qquad\qquad\ \ \ \ \ \ \ \ \ \ \ \ \ &\\42&100\ \ \ \ \quad\qquad\ \ \quad\ \ \ \ \ \ \ \qquad\quad\\\underline{\ \ \ \ 2\ \ }&\underline{\ -84\ \ \ \ \ \ \ \ \ \ \qquad}\qquad\qquad\qquad\ \\ 443&\ \ 1600\ \ \ \ \ \ \qquad\qquad\ \ \ \ \ \ \qquad\\\underline{\ \ \ \ \ \ \ 3\ \ }&\underline{-1329\qquad}\qquad\qquad\qquad\ \ \ \\4466&27100\qquad\qquad\ \ \ \ \ \ \ \ \ \quad\\ \underline{\ \ \ \ \ \ \ 6\ }&\underline{-26796\qquad}\qquad\qquad\ \ \ \ \ \ \ \\447206&3040000\qquad\qquad\\ \underline{\ \qquad \ \ 6\ }&\underline{-2683236\qquad}\qquad\ \ \ \\4472127&35676400\qquad\ \ \\ \underline{\qquad\ \ \ \ \ \ 7 \ \ }&\underline{31304889\ \ \ \ \ \ \ \ }\ \ \ \\ 44721349&437121100\ \ \ \ \\\underline{\qquad\ \ \ \ \ \ \ \ \ 9\ \ }&\underline{402492141\ \ \ \ } \\447213587&\ \ 3465895900\\ \underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7\ \ }&\qquad\underline{\ \ 3130495109\qquad}\\ 4472135947&\qquad\ 33540079100\\ \underline{\qquad\ \ \ \ \ \ \ \ \ \ \ \ \ 7\ \ } &\qquad\underline{\ 31304951624}\\ &\qquad\ \ \ \ \ 2235127471\end{array}$

$\sqrt{5} = 2.236067977...$

This is neither terminating nor repeating decimal

And therefore, $\sqrt{5}$ is not a rational number.

Answer 2

Answer:

Hey mate here is your answer

Let us assume root 5 is an rational number.

So we can find two integers a and b.

Both have common factors 1 so we divide them by 1.

:root 5 =a/b

=squaring both sides :

Root5 square =a/b square

5b square = a square

Here we can see that a square is divisible by 5 and also is divisible by a

Let a = 5 k.

Put the value of a

We have 5 b square = 5 k square

B square = 5k

So we can see th b square is divisible by 5 so b is also divisible by 5

Is. it arise contradiction that boat has Common Factor 5 A and B are coprime number and root 5 is not and rational number it is irrational number