Multiple Choice Question (MCQ)
Which one of the following is an irrational number?

×
\sqrt{9}

✓
3\sqrt{8}

×
\sqrt{100}

×
\sqrt{0.64}
Which one of the following is an irrational number?
\sqrt{9}
3\sqrt{8}
\sqrt{100}
\sqrt{0.64}
9 is the square of 3. Square root is the inverse operation of square, which results in an integer. \sqrt{9} = 3. So it's not an irrational number.
3\sqrt{8}=3\sqrt{2\cdot 4 }=6\sqrt{2}
Simplifying the number gives a number with square root of a prime number. So it is an irrational number.
\sqrt{100}=10
100 is also a perfect square. Square root of 100 gives an integer 10
\sqrt{0.64} =0.8
Square root of a decimal which is derived from an perfect square may result in a decimal, for example, 0.8 in this case. So square root of 0.64 is a rational number.