# Mathematics Questions and Answers – Square Roots by Prime Factorisation

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Square Roots by Prime Factorisation”.

1. What are the prime factors of 144?
a) 12×12
b) 12×2×6
c) 2×3×2×3×2×2
d) 3×2×3×2×3×2

Explanation: Prime factors of a number are the product of some prime numbers. Here we need to find the prime factors for 144 so we find the prime factors to be 2×3×2×3×2×2. Therefore this is the only correct option and the others are incorrect.

2. Find the prime factors of 1000.
a) 2×5×2×5×5×5
b) 2×5×2×5×2×5
c) 2×2×5×2×5×2
d) 4×5×5×2×5

Explanation: Prime factors of a number are the product of some prime numbers. Here we need to find the prime factors for 1000 so we find the prime factors to be 2×5×2×5×2×5. Therefore this is the only correct option and the others are incorrect.

3. Which of the prime factors would be correct for square of 9?
a) 3×3×9
b) 34
c) 9×9
d) 8×1

Explanation: To find prime factor for a square of any number we can find the prime factors of that number itself first and then write those prime factors twice. Here we need to find the prime factors of 92=81, now we find the prime factors of 9, we get 3×3=32. Now we square the prime factors, therefore we get 34. Therefore the correct answer is 34 and the others are incorrect.

4. Find the square root of 225by using prime factors.
a) 3×5
b) 5×5
c) 3×3
d) 15

Explanation: Here we need to find the square root of 225 which is 15. Now we need to find the prime factors of 15 and they are 3×5. Therefore the correct answer is 3×5 and the others are incorrect.

5. Prime factors of 12 are _______
a) 3×4
b) 3×2
c) 3×2×2
d) 4×2×4

Explanation: Prime factors of a number are the product of some prime numbers. Here we need to find the prime factors for 12 so we find the prime factors to be 2×2×3. Therefore this is the only correct option and the others are incorrect.

6. Two different numbers can have same prime factors.
a) True
b) False

Explanation: No two different numbers can have same prime factors as we know that product of two numbers cannot be same. Therefore the above-given statement is incorrect and hence the answer would be false.

7. Square root of 324 is ______
a) 18
b) 12
c) 22
d) 24

Explanation: Here in order to find the square root of 324, we find the prime factors of 324.
Prime factors of 324=3×3×3×3×2×2
Now we combine the same numbers in pairs,
Prime factors of 324=32×32×22
Now taking roots on both the sides we get.
Prime factors of $$\sqrt{324}$$=3×3×2…..i.e.18
Therefore the correct answer is 18 and the others are incorrect.

8. Prime factors of 41 are ____
a) 1×41
b) 4×1
c) 1×4×2
d) 2×2×1

Explanation: Here we need to find the prime factors of 41 but from our prior knowledge we know that 41 is a prime number. So the prime factors are 41×1. Hence we get our answer 41×1. Hence we conclude that the correct answer is 41×1 and the others are incorrect.

9. What are the prime factors of prime numbers?
a) The prime number itself
b) Any number depending on the prime number
c) Prime number and the number itself
d) There cannot be any prime factors

Explanation: Prime numbers can be factorized by only two numbers which are 1 and the prime number itself. So, there can only be one answer which would satisfy the condition to our question. Therefore the correct answer is Prime number and the number itself and the other options are incorrect.

10. What are prime numbers?
a) A number which has one and only one factor
b) A with only 1 as factor
c) A number which has 1 and the number itself as the factors
d) All numbers are prime numbers