Question

3. By what smallest number must 180 be multiplied so that it becomes a perfect
square? Also, find the square root of the number so obtained.
10​

Answer 1

Answer:

hope helps nice question happy Evening

Answer 2

The least number is 5 and the “square root” is 30.

Solution:

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

$180 = 2 \times 9$

$2 \times 9 \times 10$

$2 \times 3 \times 3 \times 2 \times 5$

${2}^{2} \times {3}^{2} \times 5$

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:

$180 = {2}^{2} \times {3}^{2} \times {5}^{2}$

$4 \times 9 \times 25$

$900$

Now, the square of 900 = 30

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