Question

CONTENT QUALITY Answers are required.Best answers will be brainlisted.

Answer 1

(1)

It is an irrational number. 

(2) We 1st find the average of 2 numbers.

$= \ \textgreater \ \frac{ \frac{2}{3} + \frac{5}{3} }{2}$

$= \ \textgreater \ \frac{7}{ \frac{3}{2} }$

$= \ \textgreater \ \frac{7}{6}$


Now,

$= \ \textgreater \ \frac{ \frac{2}{3} + \frac{7}{6} }{2}$

$= \ \textgreater \ \frac{11}{ \frac{6}{2} }$

$= \ \textgreater \ \frac{11}{12}$


Now,

$= \ \textgreater \ \frac{ \frac{5}{3} + \frac{7}{6} }{2}$

$= \ \textgreater \ \frac{ \frac{17}{6} }{2}$

$= \ \textgreater \ \frac{17}{12}$



Therefore the two rational numbers are 12/12, 13/12.



(3) 

$Given : \frac{1}{ \sqrt{5} }$

Multiply and divide by root 7.

$= \ \textgreater \ \frac{1}{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }$

$= \ \textgreater \ \frac{ \sqrt{5} }{( \sqrt{5} )^2}$

$= \ \textgreater \ \frac{ \sqrt{5} }{5}$




(4) 

$Given : ( \sqrt{3} - \sqrt{7} )^2$

We know that (a - b)^2 = a^2 + b^2 - 2ab

$= \ \textgreater \ ( \sqrt{3} )^2 + ( \sqrt{7} )^2 - 2( \sqrt{3}) ( \sqrt{7} )$

$= \ \textgreater \ 3 + 7 - 2 \sqrt{3* 7}$

$= \ \textgreater \ 10 - 2 \sqrt{21}$



Hope this helps!