Question

Find the value
3. Find the value of 3√81+ 3√192+ 3√375/3√24​

Answer 1

Answer:

$3√81+ 3√192+ \frac{ 3√375}{3√24}$

$(3 \times 9)+ 3 \sqrt{64 \times 2}+ \frac{ 3 \sqrt{25 \times 7} }{3 \sqrt{4 \times 6} }$

$27+ (3 \times 8) \sqrt{2}+ \frac{ (3 \times 5) \sqrt{7} }{(3 \times 2) \sqrt{6} }$

$27+ 24 \sqrt{2}+ \frac{ 5 \sqrt{7} }{2 \sqrt{6} }$

rationalization of denominator,

$27+ 24 \sqrt{2}+ \frac{ 5 \sqrt{7} \times 2 \sqrt{6} }{2 \sqrt{6} \times 2\sqrt{6} }$

$27+ 24 \sqrt{2}+ \frac{ (5 \times 2) \sqrt{7 \times 6} }{(2 \times 2) \sqrt{6 \times 6} }$

$27+ 24 \sqrt{2}+ \frac{ (5) \sqrt{42} }{(2) \sqrt{36} }$

$27+ 24 \sqrt{2}+ \frac{ 5 \sqrt{42} }{2 \times 6}$

$27+ 24 \sqrt{2}+ \frac{ 5 \sqrt{42} }{12}$

this is the most simplified answer for further calculation you need calculater