Question 14 Marks
For each of the following numbers, find the smallest whole number by which it should be multiplied, so as to get a perfect square number. Also, find the square root of the square number, so obtained.
108
108
Answer
View full question & answer→Given number is 180.
Using prime factorisation, we get
$180=2 \times 2 \times 3 \times 3 \times 5$
It is clear that in order to get a perfect square, one more 5 is required.
So, the given number should be multiplied by 5 to make the product a perfect square.
$\therefore 180 \times 5=900$ is a perfect square.
Now, $900=2 \times 2 \times 3 \times 3 \times 5 \times 5$
$\begin{aligned} & =(2 \times 3 \times 5)^2 \\ \therefore \quad \sqrt{900} & =2 \times 3 \times 5=30\end{aligned}$
Hence, the square root of 900 is 30.
Using prime factorisation, we get
$180=2 \times 2 \times 3 \times 3 \times 5$
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
So, the given number should be multiplied by 5 to make the product a perfect square.
$\therefore 180 \times 5=900$ is a perfect square.
Now, $900=2 \times 2 \times 3 \times 3 \times 5 \times 5$
$\begin{aligned} & =(2 \times 3 \times 5)^2 \\ \therefore \quad \sqrt{900} & =2 \times 3 \times 5=30\end{aligned}$
Hence, the square root of 900 is 30.