Square Root And Cube Root - Study Mode

[#91] The value of $$sqrt 2 $$ xa0 up to three places of decimal is = ?
Correct Answer

(D) 1.414

Explanation

Solution: $$eqalign{
& ,,,,,,,,,,1|overline 2 ,.,,overline {00} ,,overline {00} ,,overline {00} ,(1.414 cr
& ,,,,,,,,,,,,,|1 cr
& ,,,,,,,,,,,,,| - - - - - - - - cr
& ,,,,,,24|,,1,00 cr
& ,,,,,,,,,,,,,|,,,,96 cr
& ,,,,,,,,,,,,,| - - - - - - - - cr
& ,,,281,|,,,,,,,,,400 cr
& ,,,,,,,,,,,,,|,,,,,,,,281 cr
& ,,,,,,,,,,,,,| - - - - - - - cr
& 2824,|,,,,,,,,,,,,,,,,11900 cr
& ,,,,,,,,,,,,,|,,,,,,,,,,,,,,,11296 cr
& ,,,,,,,,,,,,,| - - - - - - - cr
& herefore sqrt 2 = 1.414 cr} $$

[#92] If $$3sqrt 5 + sqrt {125} = 17.88{ ext{,}}$$ xa0 xa0 then what will be the value of $$sqrt {80} $$xa0 $$ + $$ $$6sqrt 5 $$xa0 = ?
Correct Answer

(D) 22.35

Explanation

Solution: $$eqalign{
& Rightarrow 3sqrt 5 + sqrt {125} = 17.88 cr
& Rightarrow { ext{ }}3sqrt 5 + sqrt {25 imes 5} = 17.88 cr
& Rightarrow { ext{ }}3sqrt 5 + 5sqrt 5 = 17.88 cr
& Rightarrow { ext{ }}8sqrt 5 = 17.88 cr
& Rightarrow sqrt 5 = 2.235 cr
& herefore sqrt {80} + 6sqrt 5 cr
& = sqrt {16 imes 5} + 6sqrt 5 cr
& = 4sqrt 5 + 6sqrt 5 cr
& = 10sqrt 5 cr
& = left( {10 imes 2.235}
ight) cr
& = 22.35 cr} $$

[#93] Given $$sqrt 2 = 1.414.$$ xa0 Then the value of $$sqrt 8 $$xa0 $$ + $$ $$2sqrt {32} $$xa0 $$ - $$ $$3sqrt {128} $$xa0 $$ + $$ $$4sqrt {50} $$ xa0 is = ?
Correct Answer

(B) 8.484

Explanation

Solution: Given expression, $$sqrt {4 imes 2} + 2sqrt {16 imes 2} - 3sqrt {64 imes 2} $$ xa0 xa0 xa0 $$ + $$ $$4sqrt {25 imes 2} $$ $$eqalign{
& = 2sqrt 2 + 8sqrt 2 - 24sqrt 2 + 20sqrt 2 cr
& = 6sqrt 2 cr
& = 6 imes 1.414 cr
& = 8.484 cr} $$

[#94] The approximate value of $$frac{{3sqrt {12} }}{{2sqrt {28} }}$$xa0 $$ div $$ $$frac{{2sqrt {21} }}{{sqrt {98} }}$$ xa0 is ?
Correct Answer

(A) 1.0605

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& = frac{{3sqrt {12} }}{{2sqrt {28} }} imes frac{{sqrt {98} }}{{2sqrt {21} }} cr
& = frac{{3sqrt {4 imes 3} }}{{2sqrt {4 imes 7} }} imes frac{{sqrt {49 imes 2} }}{{2sqrt {21} }} cr
& = frac{{6sqrt 3 }}{{4sqrt 7 }} imes frac{{7sqrt 2 }}{{2sqrt {21} }} cr
& = frac{{21sqrt 6 }}{{4sqrt {7 imes 21} }} cr
& = frac{{21sqrt 6 }}{{28sqrt 3 }} cr
& = frac{3}{4}sqrt 2 cr
& = frac{3}{4} imes 1.414 cr
& = 3 imes 0.3535 cr
& = 1.0605 cr} $$

[#95] $$sqrt {110.25} imes sqrt {0.01} , div $$ xa0xa0 $$sqrt {0.0025} $$ xa0 $$ - $$ $$sqrt {420.25} $$ xa0equals ?
Correct Answer

(A) 0.50

Explanation

Solution: Given expression, $$ = sqrt {frac{{11025}}{{100}}} imes sqrt {frac{1}{{100}}} , div ,$$ xa0xa0 $$sqrt {frac{{25}}{{10000}}} , - ,$$ $$,sqrt {frac{{42025}}{{100}}} $$ $$eqalign{
& = frac{{105}}{{10}} imes frac{1}{{10}} div frac{5}{{100}} - frac{{205}}{{10}} cr
& = frac{{105}}{{100}} imes frac{{100}}{5} - frac{{205}}{{10}} cr
& = 21 - frac{{205}}{{10}} cr
& = frac{{210 - 205}}{{10}} cr
& = frac{5}{{10}} cr
& = frac{1}{2} cr
& = 0.50 cr} $$