Prime Factorization for Finding Perfect Square

Q. Determine whether $441$ is a perfect square using prime factorization.

1. Yes, $441$ is a perfect square.
2. No, $441$ is a not perfect square.

Q.

Find the square root of $32$.

Q. The smallest perfect square using the first three prime numbers as factors is .

Q. The perfect square of a number is always

1. Positive
2. Negative
3. positive or negative
4. None of these

Q. Find the number(s) that can be multiplied with $672$ to make it a perfect square.

1. $24$
2. $42$
3. $168$
4. $186$

Q. Square root of 324 is

1. 14
2. 15
3. 17
4. 18

Q. 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.

1. $a\to b\to c$
2. $c\to a\to b$
3. None of the above.

Q. Identify the correct pairs of perfect square and square root.

1. 121
2. 196
3. 64
4. 16
5. 11
6. 14
7. 8
8. 4

Q. The factorization of a number is $2\times 2\times 6\times 9\times 24.$ Is this number a perfect square? Answer in Yes/ No.

Q. 225 is a perfect square number because the number equals the product of 15 multiplied by

1. 1
2. 9
3. 225
4. 15