Question

Is the number √0.0036 rational or irrational? What about the number√3.6? Explain your reasoning.
pls help thx

Answer 1

Answer:

√0.0036=0.06 its rational it can be written as 3/50

√3.6=√36/10=6/√10

√10 cant be written as p/q form so it is irrational

#600th solution

Answer 2

Basic Concept :-

What are irrational numbers?

• Irrational numbers are the real numbers that cannot be expressed in the form of p/q, where p and q are integers, q≠0.

• The decimal expansion of an irrational number is neither terminating nor repeating. 

• For example, √2, √3, √5, √6, √7 etc., are irrational

• Basically, non - perfect squares numbers are irrational.

What is a Rational Number?

• A rational number can be defined as a number which can be represented in the form of p/q where q ≠ 0.  

• The decimal form of rational numbers may be either terminating decimal or the non terminating but repeating decimal. 

• In rational numbers, if denominator can be factorized as a factors of 2 and 5, then its decimal representation is terminating otherwise non - terminating but repeating.

Let's solve the problem now!!

Consider,

$\rm :\longmapsto\: \sqrt{0.0036}$

$\: \sf \: \: = \: \: \sqrt{\dfrac{36}{10000} }$

$\: \sf \: \: = \: \: \sqrt{\dfrac{6 \times 6}{100 \times 100} }$

$\: \sf \: \: = \: \: \dfrac{6}{100}$

$\: \sf \: \: = \: \: 0.06$

$\rm \: Since \: decimal \: representation \: of \: \sqrt{0.0036} \: is \: terminating$

$\bf\implies \: \sqrt{0.0036} \: is \: rational$

Now,

Consider,

$\rm :\longmapsto\: \sqrt{3.6}$

Please see the attachment

$\rm \: Since \: decimal \: representation \: of \: \sqrt{3.6} \: is \: non \: terminating \: and \: non \: repeating$

$\bf\implies \: \sqrt{3.6} \: is \: irrational$