Question
Find the smallest whole number with which $252$ should be divided so as to get a perfect square. Also find the square root of the square number so obtained.
✓
Answer
The prime factorisation of $252$ is $252 = 2$ $\times$ $2$ $\times$ $3$ $\times$ $3$ $\times$ $7$
We see that prime factor $7$ has no pair. So, if we divide $252$ by $7$, then we get
$\frac {252 }{ 7}$ $= 2$ $\times$ $2$ $\times$ $3$ $\times$ $3$
Now each prime factor has a pair. Therefore, $\frac {252 }{ 7}$ $= 36$ is a perfect square.
Thus, the required smallest number is $7$.
Hence, $\sqrt {36} $ $= 2$ $\times$ $3 = 6$.
We see that prime factor $7$ has no pair. So, if we divide $252$ by $7$, then we get
$\frac {252 }{ 7}$ $= 2$ $\times$ $2$ $\times$ $3$ $\times$ $3$
Now each prime factor has a pair. Therefore, $\frac {252 }{ 7}$ $= 36$ is a perfect square.
Thus, the required smallest number is $7$.
Hence, $\sqrt {36} $ $= 2$ $\times$ $3 = 6$.
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