Question

which of the following in an irrational number

a) root 16
b) root 12
c) root 12/3
d) root 100


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Answer 1

Answer:

option (b) is correct. √12 is an irrational number.

Answer 2

The number √12 is irrational.

Option b is correct.

Given:

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

To find:

• Which of the above written 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:$\sqrt{12}$

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

or

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

or

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

thus,

√3 is not integer.

So,

Option b) is irrational number.

Step 3:

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

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

or

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

or

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

Thus,

Option c is rational number.

Step 4:

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

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

or

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

Thus,

Option d is rational.

Thus,

The number √12 is irrational.

Option b is correct.

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