Question

the number ( 1 + root 2 ) square is ​

Answer 1

Step-by-step explanation:

No. We can prove that by contradiction. Let 1/sqrt(2) be rational and

1/sqrt(2)=m/(m+n) . . . . . .(1) where m, n are non-zero integers.

inverting and squaring both sides we write

2 =(m+n)^2 /( m^2) . . . . . . .(2)

2m^2 = m^2 + n^2 +2mn . . .(3) or

m^2 - 2nm - n^2 = 0 . . . . . . . . . . . .(4)

(m - n)^2 + n^2 + n^2 = 0 . . . . . . . . . . . (5)

(5) can not be true since all three terms are positive integers.

hence (1) is not true and 1/sqrt(2) is not rational.

Answer 2

Answer:

Root 2 = 1 . 41 upon root two equal to one upon 1.41 . 1/root 2 * root 2 * root 2 . 2 root upon 2= 1.41 / 2 .

Step-by-step explanation: