Square Root And Cube Root - Study Mode

[#41] $$sqrt {176 + sqrt {2401} } $$ xa0xa0 is equal to = ?
Correct Answer

(B) 15

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& = sqrt {176 + 49} cr
& = sqrt {225} cr
& = 15 cr} $$

[#42] $${left( {15}
ight)^2} + {left( {18}
ight)^2} - 20 = sqrt ? $$
Correct Answer

(D) 279841

Explanation

Solution: $$eqalign{
& { ext{Let, }} cr
& {left( {15}
ight)^2} + {left( {18}
ight)^2} - 20 = sqrt x cr
& { ext{Then, }} cr
& sqrt x = 225 + 324 - 20 cr
& Leftrightarrow x = {left( {529}
ight)^2} cr
& Leftrightarrow x = 279841 cr} $$

[#43] $$sqrt ? imes sqrt {484} = 1034$$
Correct Answer

(B) 2209

Explanation

Solution: $$eqalign{
& { ext{Let}}, cr
& sqrt x imes sqrt {484} = 1034 cr
& { ext{Then}}, cr
& sqrt x imes 22 = 1034 cr
& Leftrightarrow sqrt x = frac{{1034}}{{22}} = 47 cr
& Leftrightarrow x = {left( {47}
ight)^2} cr
& Leftrightarrow x = 2209 cr} $$

[#44] $$sqrt {11881} imes sqrt ? = 10137$$
Correct Answer

(B) 8649

Explanation

Solution: $$eqalign{
& { ext{Let}}, cr
& sqrt {11881} imes sqrt x = 10137 cr
& { ext{Then}}, cr
& 109 imes sqrt x = 10137 cr
& Leftrightarrow sqrt x = frac{{10137}}{{109}} = 93 cr
& Leftrightarrow x = {left( {93}
ight)^2} cr
& Leftrightarrow x = 8649 cr} $$

[#45] In the equation $$frac{{4050}}{{sqrt x }} = 450{ ext{,}}$$ xa0 the value of x is = ?
Correct Answer

(C) 81

Explanation

Solution: $$eqalign{
& frac{{4050}}{{sqrt x }} = 450 cr
& Leftrightarrow sqrt x = frac{{4050}}{{450}} cr
& Leftrightarrow sqrt x = 9 cr
& Leftrightarrow x = {left( 9
ight)^2} cr
& Leftrightarrow x = 81 cr} $$