Surds And Indices - Study Mode
[#136] $$2
oot 3 of {32} - 3
oot 3 of 4 +
oot 3 of {500} = ?$$
Correct Answer
(C) $$6
oot 3 of 4 $$
Explanation
Solution: $$eqalign{
& 2
oot 3 of {32} - 3
oot 3 of 4 +
oot 3 of {500} cr
& = 2
oot 3 of {{2^3} imes 4} - 3
oot 3 of 4 +
oot 3 of {{5^3} imes 4} cr
& = 2 imes 2
oot 3 of 4 - 3
oot 3 of 4 + 5
oot 3 of 4 cr
& = 9
oot 3 of 4 - 3
oot 3 of 4 cr
& = 6
oot 3 of 4 cr} $$
[#137] The least one among $${ ext{2}}sqrt 3 { ext{,}}$$xa0 $${ ext{2}}
oot 4 of 5 { ext{,}}$$xa0 $$sqrt 8 { ext{,}}$$xa0 $${ ext{3}}sqrt 2 $$xa0 is = ?
Correct Answer
(C) $$sqrt 8 $$
Explanation
Solution: $$2sqrt 3 = {left( {4 imes 3}
ight)^{frac{1}{2}}} o {12^{frac{1}{2}}} o {12^{frac{2}{4}}} o
oot 4 of {144} $$ $$2
oot 4 of 5 =
oot 4 of {left( {5 imes 16}
ight)} o {80^{frac{1}{4}}} o
oot 4 of {80} $$ $$sqrt 8 = {8^{frac{1}{2}}} o {8^{frac{1}{2}}} o x08oxed{
oot 4 of {64} },{ ext{smallest}}$$ $$3sqrt 2 = sqrt {18} o {18^{frac{1}{2}}} o {18^{frac{2}{4}}} o
oot 4 of {324} $$ $$sqrt 8 ,{ ext{ is answer}}$$
[#138] The greatest one of $$sqrt 2 ,$$xa0 $$
oot 3 of 3 ,$$xa0 $$
oot 6 of 6 ,$$xa0 $$
oot 5 of 5 $$xa0 is = ?
Correct Answer
(B) $$
oot 3 of 3 $$
Explanation
Solution: $$eqalign{
& sqrt 2 o {2^{frac{1}{2}}} o {2^{frac{{15}}{{30}}}} =
oot {30} of {{2^{15}}} =
oot {30} of {32768} cr
&
oot 3 of 3 o {3^{frac{1}{3}}} o {3^{frac{{10}}{{30}}}} =
oot {30} of {{3^{10}}} =
oot {30} of {59049} cr
&
oot 6 of 6 o {6^{frac{1}{6}}} o {6^{frac{5}{{30}}}} =
oot {30} of {{6^5}} =
oot {30} of {7776} cr
&
oot 5 of 5 o {5^{frac{1}{5}}} o {5^{frac{6}{{30}}}} =
oot {30} of {{5^6}} =
oot {30} of {15625} cr
& { ext{So }}
oot 3 of 3 { ext{ is the greatest}}{ ext{.}} cr} $$
[#139] The greatest among the numbers $${left( {2.89}
ight)^{0.5}},$$ xa0 $$2 - {left( {0.5}
ight)^2},$$ xa0 $$1 + frac{{0.5}}{{1 - frac{1}{2}}},$$ xa0 $$sqrt 3 $$xa0 is = ?
Correct Answer
(C) $$1 + frac{{0.5}}{{1 - frac{1}{2}}}$$
Explanation
Solution: $$eqalign{
& {left( {2.89}
ight)^{0.5}} = {left( {2.89}
ight)^{frac{5}{{10}}}} o sqrt {2.89} o 1.7 cr
& { ext{2}} - {left( {0.5}
ight)^2} = 2 - 0.25 o 1.75 cr
& 1 + frac{{0.5}}{{1 - frac{1}{2}}} = 1 + frac{{0.5}}{{0.5}} o 1 + 1 o 2 leftarrow { ext{Greatest}} cr
& sqrt 3 = 1.732 cr} $$
[#140] The greatest of $$sqrt 2 ,$$ xa0$$
oot 6 of 3 ,$$ xa0$$
oot 3 of 4 ,$$ xa0$$
oot 4 of 5 $$ xa0 is = ?
Correct Answer
(B) $$
oot 3 of 4 $$
Explanation
Solution: LCM of 2, 3, 4, 6 is 12 $$sqrt 2 = $$xa0 $${2^{frac{1}{2}}} = $$xa0 $${2^{left( {frac{1}{2} imes frac{6}{6}}
ight)}} = $$ xa0 $${2^{frac{6}{{12}}}} = $$xa0 $${left( {{2^6}}
ight)^{frac{1}{{12}}}} = $$xa0 $${left( {64}
ight)^{frac{1}{{12}}}} = $$ xa0 $$
oot {12} of {64} $$ $$
oot 6 of 3 = $$xa0 $${3^{frac{1}{6}}} = $$xa0 $${3^{left( {frac{1}{6} imes frac{2}{2}}
ight)}} = $$ xa0 $${3^{frac{2}{{12}}}} = $$xa0 $${left( {{3^2}}
ight)^{frac{1}{{12}}}} = $$xa0 $${left( 9
ight)^{frac{1}{{12}}}} = $$ xa0 $$
oot {12} of 9 $$ $$
oot 3 of 4 = $$xa0 $${4^{frac{1}{3}}} = $$xa0 $${4^{left( {frac{1}{3} imes frac{4}{4}}
ight)}} = $$xa0 $${4^{frac{4}{{12}}}} = $$xa0 $${left( {{4^4}}
ight)^{frac{1}{{12}}}} = $$xa0 $${left( {256}
ight)^{frac{1}{{12}}}} = $$ xa0 $$
oot {12} of {256} $$ $$
oot 4 of 5 = $$xa0 $${5^{frac{1}{4}}} = $$xa0 $${5^{left( {frac{1}{4} imes frac{3}{3}}
ight)}} = $$ xa0 $${5^{frac{3}{{12}}}} = $$xa0 $${left( {{5^3}}
ight)^{frac{1}{{12}}}} = $$xa0 $${left( {125}
ight)^{frac{1}{{12}}}} = $$ xa0 $$
oot {12} of {125} $$ Clearly $$
oot {12} of {256} ,,i.e.,
oot 3 of 4 $$ xa0 xa0 is the greatest.