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Square Root

What Is the Square Root of 225? How to Find the Square Root of 225?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 225? How to Find the Square Root of 225?

What Is the Square Root of 225? How to Find the Square Root of 225?

The square root of 225 is 15. When the addition is inversed we get subtraction, when multiplication is inversed we get division when we inverse the square root of a number we get by squaring the values. When a value is multiplied by itself we get the original value. Let us take 225 as an example.

When the number 15 is multiplied by itself (15×15) we get 225 and by squaring 152 we get 225. They are denoted as a rational symbol √ and the exponential form is expressed as (15)0.5 or (15)½ since p/q ≠ 0 and they have a whole number as their quotient they are rational and a perfect square number.

Methods to find the square root of 225

There are three methods to find the square root of the number for the rational and perfect square values. 

  • Long division method
  • Prime factorization method
  • Repeated subtraction

Long division method

The long division operates by taking the nearest integer when divided gives the number. The division is continued for perfect square numbers until zero is reached.

Long division method
Long division method

Hence, √225 = 15

Prime factorization method

Prime factorization is one of the easiest ways to find the square root of a number. 

  • Step 1: Find the prime factors of 225
    • The prime factors of 225 = 3×3×5×5
  • Step 2: Square the similar factors n2
    • √225 = 32 × 52
  • Step 3: Multiply the squares
    • 225 = 3 × 5
    • Hence, √225 = 15

Repeated subtraction method

Repeated subtraction is carried out by subtracting the number that is odds. The step is continued until zero is obtained. 

  1. 225 – 1 = 224
  2. 224 – 3 = 221
  3. 221 – 5 =  216
  4. 216 – 7 = 209
  5. 209 – 9 = 200
  6. 200 – 11= 189
  7. 189 – 13 = 176
  8. 176 – 15 = 161
  9. 161 – 17 = 144
  10. 144 – 19 = 125
  11. 125 – 21 = 104
  12. 104 – 23 = 81
  13. 81 – 25 = 56
  14. 56 – 27 =  29
  15. 29 – 29 = 0

The step in which zero is obtained is the 15th one
Hence, √225 = 15

Solved examples

Q1: If the area of the circle is 225 π square inches find the radius of the circle.
A1: Area of the square = πr2
πr2 = 225π
Since π is common we will cancel that 
We get r2 = 225
r= √225 
The radius of the circle is 15 inches. 

Q2: Solve 2 √225 + 1  √225
A2: The square root of 225 = 15
=2 (15) + 1 (15)
= 30+15
=45

Q3: Class C has 225 students if the number of students to be seated should be equal in the same row and column. how many students can sit in a row?
A3: The total number of students = 225
When they need to be seated equally then the number has to be equally split,
By taking the square root 225 we get 15
Hence, 15 people are seated equally in both rows and columns.

Q4: Stacy wants to simply 225 to its simplest form, let’s help her.
A4: 225 = 32 ×52
√225 = 15

Q5: what is the value of x if x225 = 60
A5: x225 = 60
225 = 15
Hence, x 15 = 60
X = 60/15 = 6.6
Therefore x = 6.6.

Frequently asked questions

What is the square root of 225?
225 = 32 ×52
√225 = 15
The square root of 225 = 15.

Explain why the square root of 225 is a rational number
When finding the prime factor of 225 we get 152 which is entirely an even power hence all the numbers are positive integers which makes them rational numbers.

What is the value of 225 and the square root of 225?
The square root of 225 is 15,
therefore 225√225
225 × 15 = 3375

What is the real value for the square root of 225
The actual value for the 225 = 15.
When the number 15 is multiplied by itself (15×15) we get 225 and by squaring 152 we get 225.

What is the square root of 900?
The prime factor of 900 = 2 × 2 × 3 × 3 × 5 × 5 
The square root of 900 = 30

What is the square root of (-225)?
The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.1
Hence, the √225 = 15i

Is 225 a perfect square number?
Yes, 225 is a perfect square number.
When the square root of the number is squared we get the given number.

We hope that this article has helped you in clearing your queries on the square root of 225!

Written by

Prerit Jain

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