Question

Prove that 2+root7 is irrational

Answer 1

Step-by-step explanation:

▪️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.

Hopes it help you❤️❤️

Answer 2

Answer:

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