Question

PROVE (ROOT2+2)^2 AS RATIONAL OR IRRATIONAL

Answer 1

Answer:

it is irrational

Step-by-step explanation:

(√2+2)^2

(√2)^2 +2^2+2×√2×2

2+4+4√2

6+4√2

Answer 2

Answer: Irrational number

Step-by-step explanation:

$6+4\sqrt{2} =a/b\\Let it be arationalnumber\\4\sqrt{2} =a-6b/b\\\sqrt{2} =a-6b/4b$

a-6b/4b is a rational number

therefore $\sqrt{2}$ is a rational number which controdicts the fact that $\sqrt{2}$ is a irrational number.

Therefore our assumtion was wrong.

Therefore, $(\sqrt{2} +2)^{2}$is not a rational number.

Therefore, it is an irrational number.

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