Question

find the smallest number by which 3645 must be multiplied to get a perfect square?

Answer 1

We will find the prime factors of 3645


3645 => 3 × 3 × 3 × 3 × 3 × 3 × 5


Here, 5 is not in pair.


$\therefore{}$5 should be multiplied to 3645


Check :-

3645 × 5 = 18225


Square root of 18225 is 135



Hence, proved.

Answer 2

Answer:

The required smallest number by which 3645 must be multiplied to get a perfect square is 5.      

Step-by-step explanation:

To find : The smallest number by which 3645 must be multiplied to get a perfect square?

Solution :

First we factor the 3645

3 | 3645

3 | 1215

3 | 405

3 | 135

3 | 45

3 | 15

5 | 5

  |  1

$3645=3\times3 \times 3 \times 3 \times 3 \times3 \times 5$

$3645=3^2 \times 3^2 \times 3^2 \times 5$

If we pair of 2, 3 has 3 pairs and 5 is left alone.

So, If 5 is multiplied to the number then the number form is the perfect square.

Multiply both side by 5,

$3645\times 5=3^2 \times 3^2 \times 3^2 \times 5^2$

$18225=(3\times 3 \times 3\times 5)^2$

$18225=(135)^2$

Therefore, The required smallest number by which 3645 must be multiplied to get a perfect square is 5.