Question

*Which of the following is an irrational number ?*

1️⃣ √81
2️⃣ √18
3️⃣ 1/8
4️⃣ 1.8​

Answer 1

Answer:

√18 is the correct answer

Answer 2

Solution :-

Checking all given options we get,

1) √81

→ √81

→ √(±9)²

→ ± 9

→ (9/1) or (-9/1)

since it can be written in the form of p/q where q ≠ 0, it is a rational number .

2) √18

→ √18

→ √(2 * 3 * 3)

→ 3√2

since √2 is not a perfect square number . And we know that, If a square root is not a perfect square, then it is considered an irrational number .

then,

→ Rational * Irrational = Irrational .

therefore,

→ 3√2 = An Irrational Number .

3) 1/8

→ 1/8

since it can be written in the form of p/q where q ≠ 0, it is a rational number .

4) 1.8

→ 1.8

→ 18/10

→ 9/5

since it can be written in the form of p/q where q ≠ 0, it is a rational number .

Hence, we can conclude that, Option (2) √18 is an irrational number .

Learn more :-

prove that √2-√5 is an irrational number

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