Square Root of 1225
The square root of 1225 is a number whose product with itself results in 1225. The mathematical operation square root is the inverse of square. The square root of a number can be positive or negative, rational or irrational, real or imaginary. In this minilesson, we will calculate the square root of 1225 using different methods and will look at some interesting problems related to it.
 Square root of 1225: 35
 Square of 1225: 1500625
1.  What Is the Square Root of 1225? 
2.  Is Square Root of 1225 Rational or Irrational? 
3.  How to Find the Square Root of 1225? 
4.  Important Notes on Square Root of 1225 
5.  FAQs on Square Root of 1225 
What Is the Square Root of 1225?
 The square root is the number (integer) which when multiplied by itself results in the original number.
 1225 = a × a = 35^{2}
 Then a = √1225 = √(35× 35)
 35× 35= 1225 or 35 × 35 = 1225
 The 2nd root of 1225 is +35 or 35.
 This shows that 1225 is a perfect square.
Is Square Root of 1225 Rational or Irrational?
 A rational number is defined as a number that can be written in the ratio of two integers, that is, p/q where q ≠ 0.
 35 and 35 can be written as 35/1 and 35/1.
 Both numbers can be represented in the form of rational numbers.
 So, the square root of 1225 is a rational number.
How to Find the Square Root of 1225?
The square of 1225 can be calculated using the prime factorization method, long division method, or repeated subtraction method.
Square Root of 1225 by Repeated Subtraction Method
Sr. No. 
Subtraction 
12 
1104  23 = 1081 
24 
696  47 = 649 
1 
1225  1 = 1224 
13 
1081  25 = 1056 
25 
649  49 = 600 
2 
1224  3 = 1221 
14 
1056  27 = 1029 
26 
600  51 = 549 
3 
1221  5 = 1216 
15 
1029  29 = 1000 
27 
549  53 = 496 
4 
1216  7 = 1209 
16 
1000  31 = 969 
28 
496  55 = 441 
5 
1209  9 = 1200 
17 
969  33 = 936 
29 
441  57 = 384 
6 
1200  11 = 1189 
18 
936  35 = 901 
30 
384  59 = 325 
7 
1189  13 = 1176 
19 
901  37 = 864 
31 
325  61 = 264 
8 
1176  15 = 1161 
20 
864  39 = 825 
32 
264  63 = 201 
9 
1161  17 = 1144 
21 
825  41 = 784 
33 
201  65 = 136 
10 
1144  19 = 1125 
22 
784  43 = 741 
34 
136  67 = 69 
11 
1125  21 = 1104 
23 
741  45 = 696 
35 
69  69 = 0 
So, starting from 1225, we have subtracted 35 times to get 0.
Thus the square root of 1225 is 35.
Square Root of 1225 by Long Division Method
Follow the steps shown below to find the square root of 1225 by the long division method:
 Step 1. Write 1225 as shown in the figure. Pair the number in pairs from the right end by putting a bar on top of them. In the case of 1225, 25 and 12 are the two pairs starting from the right.
 Step 2. Find a number such that when it is multiplied by itself it results in a number equal to or less than 12. Here the number is 3.
 Step 3. We have the remainder and the quotient as 3. Bring down the next pair of numbers. Here it is 25. Our new dividend is 325 and divisor is (3 + 3 = 6).
 Step 4. Choose a number(n) for the unit’s place of the divisor such that 6n × n ≤ 325.
Here the number(n) is 5 as 65 × 5 = 325.
So, the square root of 1225 by the long division method is 35.
Explore square roots using illustrations and interactive examples.
Important Notes:
 The square root of 1225 is represented as √1225 in radical form.
 The square root of 1225 is represented as (1225)^{1/2} in exponential form.
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits
Square Root of 1225 Solved Examples

Example 1: Paul wants to find the square root of 1225 using the prime factorization method. Can you help Paul?
Solution:
The following steps can be followed to find the square root of 1225 using prime factorization: Step 1. Determine the prime factorization of 1225
 1225 = 5 × 5 × 7 × 7
 1225 = 52 × 72
 Step 2. Group the prime factors of 1225 in pairs.
 1225 = 52 × 72
 Step 3. Pick one factor from each pair and the square root of 1225 can be written as:
 √1225 = √(52 × 72)
 √1225 = √(5 × 7)2
 √1225 = ((5 × 7)2)1/2 = ±(5 × 7)
 √1225 = ±35

Example 2: Ryan is working on a squareshaped table with a surface area of 1225 square inches. He wants to add a protective layer around the sides of the table. The cost of adding a protective layer per inch is given as $0.50. How much will it cost Ryan to add a protective layer around the table?
Solution:
The surface area of the squareshaped table = 1225 square inches
Length of one side = √1225 inches = 35 inches
Length of protective layer required = 35 × 4 = 140 inches
Cost of adding protective layer = 140 × 0.50 = $70.
FAQs on Square Roots of 1225
Is the square root of 1225 a rational number?
Yes, the square root of 1225 is a rational number.
The square root of 1225 is 35 and 35, both of which are rational numbers.
What is the prime factorization of 1225?
Prime factorization of 1225: 5^{2} × 7^{2}
What is the square of 1225?
The square of 1225 is (1225)^{2} = 1500625.
By what different methods we can find the square root of 1225?
We can find the square root of 1225 by the following methods:
 Long division method
 Prime factorization
 Repeated subtraction method
What is the square root of 1225?
The square root of negative numbers is imaginary.
It is represented as √1225 = 35i. (where i = √1)
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