Square Root And Cube Root - Study Mode

[#46] $$sqrt {frac{{16}}{{25}}} imes sqrt {frac{?}{{25}}} imes frac{{16}}{{25}} = frac{{256}}{{625}}$$
Correct Answer

(C) 16

Explanation

Solution: $$eqalign{
& { ext{Let}}, cr
& sqrt {frac{{16}}{{25}}} imes sqrt {frac{x}{{25}}} imes frac{{16}}{{25}} = frac{{256}}{{625}} cr
& { ext{Then}}, cr
& frac{4}{5} imes frac{{sqrt x }}{5} imes frac{{16}}{{25}} = frac{{256}}{{625}} cr
& Leftrightarrow frac{{64sqrt x }}{{625}} = frac{{256}}{{625}} cr
& Leftrightarrow sqrt x = frac{{256}}{{625}} imes frac{{625}}{{64}} cr
& Leftrightarrow x = {4^2} cr
& Leftrightarrow x = 16 cr} $$

[#47] The square root of $$left( {{{272}^2} - {{128}^2}}
ight)$$ xa0 is = ?
Correct Answer

(C) 240

Explanation

Solution: $$eqalign{
& = sqrt {left( {{{272}^2} - {{128}^2}}
ight)} cr
& = sqrt {left( {272 + 128}
ight)left( {272 - 128}
ight)} cr
& = sqrt {400 imes 144} cr
& = sqrt {57600} cr
& = 240 cr} $$

[#48] If $$y = 5{ ext{,}}$$ xa0 then what is the value of $$10ysqrt {{y^3} - {y^2}} $$ xa0 = ?
Correct Answer

(D) 500

Explanation

Solution: $$eqalign{
& = 10ysqrt {{y^3} - {y^2}} cr
& = 10 imes 5sqrt {{5^3} - {5^2}} cr
& = 50 imes sqrt {125 - 25} cr
& = 50 imes sqrt {100} cr
& = 50 imes 10 cr
& = 500 cr} $$

[#49] $$sqrt {frac{{25}}{{81}} - frac{1}{9}} = ?$$
Correct Answer

(B) $$frac{4}{9}$$

Explanation

Solution: $$eqalign{
& = sqrt {frac{{25}}{{81}} - frac{1}{9}} cr
& = sqrt {frac{{25 - 9}}{{81}}} cr
& = sqrt {frac{{16}}{{81}}} cr
& = frac{{sqrt {16} }}{{sqrt {81} }} cr
& = frac{4}{9} cr} $$

[#50] $${left[ {{{left( {sqrt {81} }
ight)}^2}}
ight]^2} = {left( ?
ight)^2}$$
Correct Answer

8

Explanation

Solution: $$eqalign{
& { ext{Let,}} cr
& {left[ {{{left( {sqrt {81} }
ight)}^2}}
ight]^2} = {left( x
ight)^2} cr
& { ext{Then,}} cr
& Leftrightarrow {x^2} = {left( {81}
ight)^2} cr
& Leftrightarrow x = 81 cr} $$