Math, asked by naniashahanu6902, 8 months ago

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

Answers

Answered by Tagoreharivardhan
23

Step-by-step explanation:

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Answered by hukam0685
0

√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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