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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 mini-lesson, 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 = 35²
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

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 square-shaped 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 square-shaped 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.

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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: 5² × 7²

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)