Simplification - Study Mode

[#196] $$frac{{
oot 3 of 8 }}{{sqrt {16} }} div sqrt {frac{{100}}{{49}}} imes
oot 3 of {125} $$ xa0 xa0xa0 is equal to = ?
Correct Answer

(B) $$1frac{3}{4}$$

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& frac{{
oot 3 of 8 }}{{sqrt {16} }} div sqrt {frac{{100}}{{49}}} imes
oot 3 of {125} , cr
& Rightarrow frac{2}{4} div frac{{10}}{7} imes 5 cr
& Rightarrow frac{2}{4} imes frac{7}{{10}} imes 5 cr
& Rightarrow frac{7}{4} cr
& Rightarrow 1frac{3}{4} cr} $$

[#197] When $$left( {frac{1}{2} - frac{1}{4} + frac{1}{5} - frac{1}{6}}
ight)$$ xa0 xa0is divided by $$left( {frac{2}{5} - frac{5}{9} + frac{3}{5} - frac{7}{{18}}}
ight){ ext{,}}$$ xa0 xa0 then the result is = ?
Correct Answer

(A) $${ ext{5}}frac{1}{{10}}$$

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& frac{{frac{1}{2} - frac{1}{4} + frac{1}{5} - frac{1}{6}}}{{frac{2}{5} - frac{5}{9} + frac{3}{5} - frac{7}{{18}}}} cr
& Rightarrow frac{{frac{{30 - 15 + 12 - 10}}{{60}}}}{{frac{{36 - 50 + 54 - 35}}{{90}}}} cr
& Rightarrow frac{{17}}{{60}} imes frac{{90}}{5} cr
& Rightarrow 5frac{1}{{10}} cr} $$

[#198] $$left{ {left( {sqrt {72} - sqrt {18} }
ight) div sqrt {12} }
ight}$$ xa0 xa0 is equal to = ?
Correct Answer

(D) $$frac{{sqrt 6 }}{2}$$

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& frac{{sqrt {72} - sqrt {18} }}{{sqrt {12} }} cr
& Rightarrow sqrt {frac{{72}}{{12}}} - sqrt {frac{{18}}{{12}}} cr
& Rightarrow sqrt 6 - sqrt {frac{6}{4}} cr
& Rightarrow frac{{sqrt 6 }}{2} cr} $$

[#199] $$1frac{3}{4} - 1frac{1}{5} + 1frac{5}{8} = ?$$
Correct Answer

(A) $$2frac{7}{{40}}$$

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& frac{7}{4} - frac{6}{5} + frac{{13}}{8} cr
& = frac{{70 - 48 + 65}}{{40}} cr
& = frac{{87}}{{40}} cr
& = 2frac{7}{{40}} cr} $$

[#200] $$1 + frac{1}{2} + frac{1}{4} + frac{1}{7} + frac{1}{{14}} + frac{1}{{28}}$$ xa0 xa0 is equal to = ?
Correct Answer

(A) 2

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& frac{{28 + 14 + 7 + 4 + 2 + 1}}{{28}} cr
& = frac{{56}}{{28}} cr
& = 2 cr} $$