Question

Match the following numbers with their squares.

• A. 11449
• B. 3969
• C. 2116
• D. 8836

Answer 1

To find the squares of numbers between 25 and 75,

• ${46}^2,50-46=4$ $\text{and}{4}^2=16$. Then, $46-25=21$

$\therefore {46}^2=2116$

• Similarly, for ${63}^2,63-50=13$ and ${13}^2=169$. Then, $63-25=38.$

So, last two digits will be 69 and before that add the residual 1 from 169 to 38 which is 38 + 1 = 39.
$\therefore {63}^2=3969$

To find the squares of numbers between 75 and 125,

• For ${94}^2$, 100 - 94 = 6 and $6^2=36.$

As $94<100$, subtract 6 from 94 i.e., 94 - 6 = 88.
$\therefore {94}^2=8836$

• Similarly, for ${107}^2$, 107 - 100 = 7 and $7^2=49$.

So, 49 will be first two digits of the square from right. As $107>100$, add 7 to 107 i.e., 107 + 7 = 114.
$\therefore {107}^2=11449$

Alternatively, 46 < 63 < 94 < 107.
So, ${46}^2<{63}^2<{94}^2<{107}^2$
$\therefore$ Match the given squares in this order.