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Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.
Given :
The given number is 147.
To do :
We have to find the smallest number by which 147 should be multiplied so as to get a perfect square and also the square root of the number so obtained.
Solution :
Prime factorisation of 147,
$147=3\times7\times7$
$= 3 \times 7^2$
To get a perfect square, we have to multiply the factors by 3.
So, $3 \times 7^2 \times 3= 3^2 \times 7^2 $
$= (3 \times 7)^2 $
$= (21)^2$
$=441$
$\sqrt{441} = \sqrt{(21)^2}$
$= 21$
Therefore, 147 has to be multiplied by 3 to get a perfect square.
The square root of 441 is 21.
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