Mathematics Multiple Choice Questions & Answers 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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