Question

by what smallestnumber must 180 be multiplied so that it becomes a perfect square also find the square root of the number so obtained​

Answer 1

Take LCM of 180

It turn out to be

2×2×3×3×5

here 5 is the only no. without pair

hence if we multiply it by five the no. thus obtained would be a perfect square

i.e.180×5=900

$\sqrt{900} = 30$

Answer 2

Answer:

Step-by-step explanation:

To find the “smallest number” by which 180 will be multiplied to get a “perfect square”, we need to factorize 180 as under:

  180 = 2 x 2 x 3 x 3 x 5

         = $2^{2} * 3^{2} * 5$

Now, 5 is not in square. If 5 is in square, then derived number will be perfect square.  

Hence, 180 must be multiplied by 5 to get a “perfect square” as shown below:

Now, 180 x 5 = 900

So, the square root of 900 = 30