**Finding the Smallest Number to Multiply 3375 to get a Perfect Square:**

To find the smallest number by which 3375 should be multiplied to get a perfect square, we need to prime factorize the given number.

1. Prime Factorization of 3375:
The prime factorization of 3375 can be obtained by dividing it by prime numbers until we reach 1. Let's start with 2:
- 3375 ÷ 2 = 1687.5 (not divisible by 2)
Moving on to the next prime number, 3:
- 3375 ÷ 3 = 1125
- 1125 ÷ 3 = 375
- 375 ÷ 3 = 125
- 125 ÷ 5 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

So, the prime factorization of 3375 is 3 × 3 × 3 × 5 × 5 × 5, which can be written as 3^3 × 5^3.

2. Identifying Odd Powers:
In order for the number to be a perfect square, all prime factors should have even powers. Let's analyze the prime factors of 3375:
- The prime factor 3 appears with an odd power of 3.
- The prime factor 5 appears with an odd power of 3.

3. Finding the Smallest Number:
To make all the powers of the prime factors even, we need to multiply 3375 by the missing prime factors and raise them to the power of 2. In this case, we need to multiply by 3^2 and 5^2.

- 3375 × 3^2 × 5^2 = 3375 × 9 × 25 = 759375

Therefore, the smallest number by which 3375 should be multiplied to get a perfect square is 759375.

**Finding the Square Root of the Resulting Number:**

To find the square root of 759375, we can use a calculator or perform the calculation manually using the long division method.

1. Using a Calculator:
By inputting 759375 into a calculator and calculating the square root, we find that the square root of 759375 is approximately 871.78.

2. Manual Calculation:
Using the long division method, we can manually calculate the square root of 759375:

- Step 1: Group the digits from right to left in pairs: 75 and 93.
- Step 2: Find the largest perfect square that is less than or equal to the leftmost group, which is 75. The largest perfect square less than 75 is 64 (8^2).
- Step 3: Divide 75 by 64, giving a quotient of 1 and a remainder of 11.
- Step 4: Bring down the next pair of digits, making it 1193.
- Step 5: Double the quotient obtained in Step 3 and put a placeholder for the digit to find. In this case, the digit is 'x': 1x.
- Step 6: Find the largest value for 'x' such that 264x multiplied by '

When we factorised 3375, we get 5×5×5×3×3××3. Hence, 15 is the smallest number by which it 3375 should be multiplied to get a perfect square.
The square root of this number would be 5×5×3×3 = 225.