Question

by what smallest number should 180 be multiplied so that it become a a perfect square​

Answer 1

Answer:

4

Step-by-step explanation:

square has four side

so

180x4 = 720

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:

$\sf 180=2 \times 90180=2×90$

$\sf =2 \times 9 \times 10=2×9×10$

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

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

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:

$180=2^{2} \times 3^{2} \times 5^{2}=4 \times 9 \times 25=900180=2$

$\therefore\textbf{Now, the square of 900 = 30}$