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Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.
Given :
The given number is 180.
To do :
We have to find the smallest number by which 180 should be multiplied so as to get a perfect square and also the square root of the perfect square so obtained.
Solution :
Prime factorisation of 180,
$180=2 \times 2\times 3\times 3\times 5 = 2^2 \times 3^2 \times 5$
To get a perfect square, we have to multiply the factors by 5.
So, $5 \times 2^2 \times 3^2 \times 5$
$ = 2^2 \times 3^2 \times 5^2 = (2 \times 3 \times 5)^2 = (30)^2=900$
$\sqrt{900} = \sqrt{(30)^2} = 30$
Therefore, 180 has to be multiplied by 5 to get a perfect square.
The square root of 900 is 30.