Question

Which of the following is an irrational number? *
1 point
a. √16
b. √(12/3)
c. √12
d. √100

Answer 1

Step-by-step explanation:

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Answer 2

√12 is an irrational number.

Option (c) is correct.

Given:

• $a) \: \: \sqrt{16}$
• $b) \: \: \sqrt{ \frac{12}{3} }$
• $c) \: \: \sqrt{12}$
• $d) \: \: \sqrt{100}$

To find:

• Which of the above written numbers is an irrational number?

Solution:

Definition to be used:

1. An irrational number can not be expressed as p/q form, where p and q are integers and q≠0.
2. A rational number can be expressed as p/q form, where p and q are integers and q≠0.

Step 1:

Check for option a: $\sqrt{16}$

we know that

$\sqrt{16} = \sqrt{( {4)}^{2} }$

and

$\sqrt{16} = 4$

or

$\sqrt{16} = \frac{4}{1}$

Thus,

Option a) is rational number.

Step 2:

Check for option b: $\sqrt{ \frac{12}{3} }$

Rewrite the number, as shown below

$\sqrt{ \frac{12}{3} } = \sqrt{ \frac{4}{1} }$

or

$\sqrt{ \frac{12}{3} } = \frac{2}{1}$

Thus,

Option (b) is a rational number.

Step 3:

Check for option c: $\sqrt{12}$

it can be written as

$\sqrt{12} = \sqrt{4 \times 3}$

or

$\sqrt{12} = \sqrt{( {2)}^{2} \times 3 }$

or

$\sqrt{12} = 2 \sqrt{3}$

As √3 is not integer. So, while writing it as

$\sqrt{12} = \frac{2 \sqrt{3} }{1}$

it is still an irrational number.

Thus,

Option (c) is irrational.

Step 4:

Check for option d: $\sqrt{100}$

It may be written as

$\sqrt{100} = \sqrt{ {(10)}^{2} }$

or

$\sqrt{100} = 10$

or

$\sqrt{100} = \frac{10}{1}$

Thus,

Option (d) is rational number.

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