Question

Which one of the following is an irrational number a)root 4 b)3root8 c)root 100 d)minus root 0.64

Answer 1

Answer:

(a) root 4 = 2

(b) 3 root 8 is not a rational number

(c) root 100 = 10

(d) - root 0.64 = -0.8

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Answer 2

Answer:

The answer is - option b)

Step-by-step explanation:

Because other than option b) all are perfect squares, so they can be operated further, that will lead to the result - rational number

Rational number = A number which can be expressed in the form P/Q form where p and q are integers and q $\neq$ 0.Moreover, a rational number is a number which has terminating or non-terminating but recurring(repeating) decimal expansion.

Irrational number = A number which cannot be expressed in the form P/Q form where p and q are integers and q $\neq$ 0.Moreover, an irrational number is a number which has non-terminating or non-recurring(repeating) decimal expansion.

See,

option a) $\sqrt{4}$

As,

$\sqrt{4}$ = 2 or 2/1 [p/q form] (RATIONAL NUMBER)

And,

option b) 3$\sqrt{8}$ (IRRATIONAL NUMBER)

As $\sqrt{8}$ is an irrational number, $\sqrt{8}$'s derivative is a non-terminating and non-repeating number

We know that

multiplication of rational number(3, here) and irrational number($\sqrt{8}$, here)

is always irrational number.

Now see,

option c) $\sqrt{100}$

As,

$\sqrt{100}$ = 10 or 10/1 [p/q form] (RATIONAL NUMBER)

see,

option d) -$\sqrt{0.64}$

As,

-$\sqrt{0.64}$ = -8 or -8/1 [p/q form] (RATIONAL NUMBER)

So WHY OPTION b) IS AN IRRATIONAL NUMBER

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