Question

Consider the steps to determine whether a number is a perfect square using prime factorization.

Step a: Determine whether each prime factor of the number can be arranged in pair.

Step b: If the prime factors can be arranged in pairs, the given number is a perfect square.

Step c: Prime factorize the number.

Arrange the steps in the correct order.

• A. $a\to b\to c$
• B. $c\to a\to b$
• C. None of the above.

Answer 1

The correct option is B $c\to a\to b$

We follow the steps in the given order to identify a perfect square number:

Step 1: Prime factorize the number.

Step 2: Determine whether each prime factor of the number can be arranged in pair.

Step 3: If the prime factors can be arranged in pairs, the given number is a perfect square.

For example, let's find out whether $400$ is a perfect square.

Step 1: Prime factorization of 400 is $4\times 10\times 10$
$=2\times 2\times 2\times 5\times 2\times 5$

Step 2: Arrange the prime factors in pairs, if possible.
$(2\times 2)\times (2\times 2)\times (5\times 5)$

Step 3: As it is possible to arrange the prime factors in pairs, we determine that $400$ is a perfect square.