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The smallest non-zero real number by which √27 should be multiplied so as to get a rational number is:
[tex]a) \: \sqrt{3} \\ b) \: \frac{1}{ \sqrt{3} } \\ c) \sqrt{13} \\ d) \sqrt{27} [/tex]
I doubt between a) and b).
Please solve this and give me the accurate answer. Step-by-step solution needed. Spam free answer required.
Thank you in advance.​

Respuesta :

mhanifa

Answer:

  • [tex]b)1/\sqrt{3}[/tex]

Step-by-step explanation:

Lets verify one-by-one:

a)

  • [tex]\sqrt{3} *\sqrt{27} =\sqrt{3*27} =\sqrt{81} = 9[/tex]

b)

  • [tex]1/\sqrt{3}*\sqrt{27} =\sqrt{1/3*27} =\sqrt{9} =3[/tex]

c)

  • [tex]\sqrt{13} *\sqrt{27} =\sqrt{13*27} =\sqrt{39*9} =3\sqrt{39}[/tex]

d)

  • [tex]\sqrt{27} *\sqrt{27} =(\sqrt{27})^2=27[/tex]

As we see in three cases we get rational number but the smallest one is 3, this indicates the answer is option b.

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