MCQs

1. The smallest number to be multiplied by 72 to make it a perfect square is

a) 2

b) 3

c) 5

2. The smallest number to be divided by 125 to make it a perfect square is

a) 25

b) 5

c) 1

3. The smallest number to be multiplied by 292 to make it a perfect square is

a) 2

b) 3

c) 7

4. The smallest number to make 1331 a perfect square is

a) 121

b) 1331

c) 11

5. The least number to be divided by 52 to make it a perfect square is

a) 13

b) 4

c) 2

6. The smallest number that should be added to the sum of the squares of 9 and 10 to make it a perfect square

a)0

b)15

c)5

7. The least no. by which 294 must be multiplied to make it a perfect square is

a) 6

b)2

c)3

8. The least number by which 1470 must be divided to get a perfect square is

a) 6

b)30

c)15

9. The smallest square number divisible by 6,9 and 15 is

a)180

b)450

c)900

10. The least number to be multiplied by each of 4,9 and 10 to make product a perfect square is

a)10

b)5

c)2

Let's solve each multiple-choice question:

1. **The smallest number to be multiplied by 72 to make it a perfect square is:**
- The prime factorization of 72 is 2^3 * 3^2.
- To make it a perfect square, we need to multiply it by 3, so the answer is (b) 3.

2. **The smallest number to be divided by 125 to make it a perfect square is:**
- The prime factorization of 125 is 5^3.
- To make it a perfect square, we need to divide it by 5, so the answer is (b) 5.

3. **The smallest number to be multiplied by 292 to make it a perfect square is:**
- The prime factorization of 292 is 2^2 * 73.
- To make it a perfect square, we need to multiply it by 73, so the answer is (c) 7.

4. **The smallest number to make 1331 a perfect square is:**
- 1331 is already a perfect square (11^2), so the answer is (a) 121.

5. **The least number to be divided by 52 to make it a perfect square is:**
- The prime factorization of 52 is 2^2 * 13.
- To make it a perfect square, we need to divide it by 13, so the answer is (a) 13.

6. **The smallest number that should be added to the sum of the squares of 9 and 10 to make it a perfect square is:**
- The sum of the squares of 9 and 10 is 81 + 100 = 181.
- The smallest number to add to make it a perfect square is 4, so the answer is (c) 5.

7. **The least number by which 294 must be multiplied to make it a perfect square is:**
- The prime factorization of 294 is 2 * 3 * 7 * 7.
- To make it a perfect square, we need to multiply it by 7, so the answer is (c) 3.

8. **The least number by which 1470 must be divided to get a perfect square is:**
- The prime factorization of 1470 is 2 * 3 * 5 * 7 * 7.
- To make it a perfect square, we need to divide it by 2 * 3 * 5 * 7, so the answer is (b) 30.

9. **The smallest square number divisible by 6, 9, and 15 is:**
- The LCM of 6, 9, and 15 is 90, which is also a perfect square, so the answer is (b) 450.

10. **The least number to be multiplied by each of 4, 9, and 10 to make the product a perfect square is:**
- The prime factorization of 4, 9, and 10 is 2^2, 3^2, and 2 * 5, respectively.
- To make the product a perfect square, we need to multiply by 5, so the answer is (c) 2.

These are the solutions to the multiple-choice questions.