Question

Prove that root 2+root 7 is not rational
number.



please answer fast
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Answer 1

Answer:

root 2+ root 7

root 2+root 7=a      (where a is an integer)

squaring both sides

(root 2+root 7)^2=(a)^2

(root 2)^2+(root 7)^+2(root 2)(root 7)=a^2

2+7+2 root 14=a^2

9+2 root 14 =a^2

2 root 14=a^2-9

root 14=a^2-9/2

since a is an integer therefore a^2-9/2 is also an integer and therefore root 14 is also an integer but integers are not rational numbers therefore root 2+root 7 is an irrational number.

proved.

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Answer 2

Answer:

prove: √7 is an irrational number. Proof: Let us assume that √7 is a rational number. So it t can be expressed in the form p/q where p,q are co-prime integers and q≠0. √7 = p/q. ...

Solving. √7 = p/q. On squaring both the side we get, => 7 = (p/q)2 => 7q2 = p2……………………………..(1)