The number of digits in the square root of 625685746009 is = ?
(A) 4
(B) 5
(C) 6
(D) 7
Solution:
The number of digits of the square root of a perfect square number of n digits is $$\eqalign{ & {\text{(i)}}\frac{n}{2}{\text{, if n is even}} \cr & {\text{(ii)}}\frac{{n + 1}}{2}{\text{, if n is odd}} \cr & {\text{Here, }}n = 12 \cr & {\text{So, required number of digits}} \cr & = \frac{n}{2} \cr & = \frac{{12}}{2} \cr & = 6{\text{ }} \cr} $$
114.
The square root of $$\left( {7 + 3\sqrt 5 } \right)$$ÃÂÃÂ $$\left( {7 - 3\sqrt 5 } \right)$$ ÃÂÃÂ is ?
The number of perfect square numbers between 50 and 1000 is = ?
(A) 21
(B) 22
(C) 23
(D) 24
Solution:
The first perfect square number after 50 is 64 $$\left( {64 = {8^2}} \right)$$ and the last perfect square number before 1000 is 961 $$\left[ {961 = {{\left( {31} \right)}^2}} \right]$$ So, the perfect squares between 50 and 1000 are the squares of numbers from 8 to 31. (31 - 8) + 1 = 24 Clearly, these are 24 in number.
116.
In the equation $$\frac{{4050}}{{\sqrt x }} = 450{\text{,}}$$ ÃÂÃÂ the value of x is = ?
(A) 9
(B) 49
(C) 81
(D) 100
Solution:
$$\eqalign{ & \frac{{4050}}{{\sqrt x }} = 450 \cr & \Leftrightarrow \sqrt x = \frac{{4050}}{{450}} \cr & \Leftrightarrow \sqrt x = 9 \cr & \Leftrightarrow x = {\left( 9 \right)^2} \cr & \Leftrightarrow x = 81 \cr} $$
117.
How many perfect squares lie between 120 and 300 ?
(A) 5
(B) 6
(C) 7
(D) 8
Solution:
$$\eqalign{ & {\left( {11} \right)^2} = 121{\text{ }} \cr & {\text{And }} \cr & {\left( {17} \right)^2} = 289 \cr} $$ So, the perfect squares between 120 and 300 are the squares of numbers from 11 to 17. Clearly, these are 7 in number.