Question

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 for class 8​

Answer 1

Answer:

45

Step-by-step explanation:

is that correct answer

Answer 2

$\red{\bf {Answer}}$

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

$\green{\bf {Solution:}}$

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

$180=2 \times 90$

$=2 \times 9 \times 10$

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

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

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:

$180=2^{2} \times 3^{2} \times 5^{2}=4 \times 9 \times 25=900$

$\boxed{\red{\sf{Now, \:the\: square \:of\: 900 \:=\: 30}}}$

Thankyou :)