Question

prove that 3+2 root 5 is irrational​

Answer 1

Answer:

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Step-by-step explanation:

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3 + 2√5 = a/ b

2√5 =a/b -3

√5 =a-3b/2b

√5 is rational.

This contradicta the fact that √5 is irrational.

So our supposition is incorrect.

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Answer 2

Answer:

$3+2\sqrt{5}$ is irrational.

Step-by-step explanation:

Prove $3+2\sqrt{5}$ is irrational

→ let's take that $3+2\sqrt{5}$ is rational number

→ so, we can write this answer as

⇒ $3+2\sqrt{5}=\frac{a}{b}$

Here a & b use two coprime number and b  ≠ 0

⇒ $2\sqrt{5} =\frac{a}{b} -3$

⇒ $2\sqrt{5} =\frac{a-3b}{b}$

∴ $\sqrt{5} =\frac{a-3b}{2b}$

Here a and b are integer so $\frac{a-3b}{2b}$ is a rational number so $\sqrt{5}$ should be rational number but $\sqrt{5}$ is a irrational number so it is contradict.

→ Hence $3+2\sqrt{5}$ is irrational.

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