Square Root And Cube Root - Study Mode

[#6] The square root of 41209 is equal to = ?
Correct Answer

(B) 203

Explanation

Solution: $$eqalign{
& ,,,,,2|4,,overline {12} ,,overline {09} ,(203 cr
& ,,,,,,,,,|4 cr
& ,,,,,,,,,| - - - - - - - - cr
& ,,40|,,,,,,,,12 cr
& ,,,,,,,,,|,,,,,,,,,,0 cr
& ,,,,,,,,,| - - - - - - - - cr
& ,,,,,,,,,|,,,,,,,,,12,09 cr
& 403|,,,,,,,,,12,09 cr
& ,,,,,,,,,| - - - - - - - - cr
& ,,,,,,,,,|,,,,,,,,,,,,x cr
& ,,,,,,,,,| - - - - - - - - , cr
& herefore sqrt {41209} = 203 cr} $$

[#7] The square root of 123454321 is = ?
Correct Answer

(C) 11111

Explanation

Solution: $$ herefore sqrt {123454321} = 11111$$

[#8] The number of digits in the square root of 625685746009 is = ?
Correct Answer

(C) 6

Explanation

Solution: The number of digits of the square root of a perfect square number of n digits is $$eqalign{
& { ext{(i)}}frac{n}{2}{ ext{, if n is even}} cr
& { ext{(ii)}}frac{{n + 1}}{2}{ ext{, if n is odd}} cr
& { ext{Here, }}n = 12 cr
& { ext{So, required number of digits}} cr
& = frac{n}{2} cr
& = frac{{12}}{2} cr
& = 6{ ext{ }} cr} $$

[#9] $$sqrt {sqrt {17956} + sqrt {24025} } = ?$$
Correct Answer

19

Explanation

Solution: $$eqalign{
& sqrt {sqrt {17956} + sqrt {24025} } cr
& = sqrt {134 + 155} cr
& = sqrt {289} cr
& = 17 cr} $$

[#10] One-fourth of the sum of prime numbers, greater than 4 but less than 16, is the square of = ?
Correct Answer

(A) 3

Explanation

Solution: Sum of prime numbers greater than 4 but less than 16 $$eqalign{
& = left( {5 + 7 + 11 + 13}
ight) cr
& = 36 cr
& herefore frac{1}{4} imes 36 cr
& = 9 cr
& = {3^2} cr} $$