Question

Divide 8√27 by 2√3. Whether quotient is a rational number?​

Answer 1

Given : Divide 8√27 by 2√3

To Find  : Whether quotient is a rational number?​

Solution:

Divide 8√27 by 2√3

8√27 ÷ 2√3

√27  = √3 x 3 x 3 x

= √3² x 3

= 3 √3

8√27 ÷ 2√3

=8 ( 3 √3 ) ÷ 2√3

= 24  ÷ 2

= 12

= 12/1

is a rational number

YES ,   quotient is a rational number

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Answer 2

SOLUTION

TO DETERMINE

Divide 8√27 by 2√3. Whether quotient is a rational number?

CONCEPT TO BE IMPLEMENTED

RATIONAL NUMBER

A Rational number is defined as a number of the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

EXAMPLE

$\displaystyle \sf{2,- 1, \frac{1}{3} , - \frac{12}{23}} \: are \: the \: examples \: of \: rational \: numbers$

EVALUATION

Here the given numbers are 8√27 and 2√3

Now

$\displaystyle \sf{ \frac{8 \sqrt{27} }{2 \sqrt{3} } }$

$\displaystyle \sf{ = \frac{8 \sqrt{3 \times 3 \times 3} }{2 \sqrt{3} } }$

$\displaystyle \sf{ = \frac{8 \times 3 \sqrt{ 3} }{2 \sqrt{3} } }$

$\displaystyle \sf{ = \frac{24 \sqrt{ 3} }{2 \sqrt{3} } }$

$\displaystyle \sf{ = 12}$

$\displaystyle \sf{ = \frac{12}{1} }$

By above concept we can conclude that the obtained number is a rational number

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