Square root of 225
Did you know, 225 is a perfect square number? Hence, when the square root of 225 is taken we will obtain an answer which is a rational number. In this lesson, we will learn to calculate the square root of 225 by long division method with solved examples and interactive questions.
 Square Root of 225: 15
 Square of 225: 50,625
1.  What Is the Square Root of 225? 
2.  Is Square Root of 225 Rational or Irrational? 
3.  How to Find the Square Root of 225? 
4.  FAQs on Square Root of 225 
What Is the Square Root of 225?
 For real numbers a and b, if a^{2 }= b, we can express a = √b
 This means that a is the second root of b.
 The square root of 225 is the inverse operation of squaring 15
 15 × 15 = 225 and 15 ×15 = 225.
 Therefore, √25 = 15
Is the Square Root of 225 Rational or Irrational?
225 can be expressed as the ratio of two integers.
As 225 can be expressed as 225 = 225/1.
Thus 225 is rational.
How to Find the Square Root of 225?
The square root of 225 can be found by various methods.
Square Root of 225 by Prime Factorization
 Get the prime factorization done for the number 225 by the ladder method or the factor tree method to get the factors.
 After getting the prime factors, arrange them in such a way that they can be expressed as a product of number x number.
 √225 = √(5 × 5 × 3 × 3)
 Squaring on both the sides, we get, √225 =√(5^{2} × 3^{2})
 This gives, 5 × 3 = 15
Square Root of 225 by Long Division Method
Here are the steps to find the square root of 225
 Step 1: Write the pair of digits starting from one's place. Here 25 is the pair.
 Step 2: On finding a divisor "n" such that n × n results in the product ≤ 2. We find 1 × 1 = 1, follow the process of long division and obtain the remainder. Here it is 1.
 Step 3: Now, bring down the next pair of numbers. Here it's 25. Multiply the quotient 1 by 2 and write it in the new divisor's place. Here it's 2.
 Step 4: Find a divisor "n" such that n × n results in the product ≤ 125. Get the next quotient place as 5. Now we get our new divisor as 25, as 5 × 125 = 225. Do the division and get the remainder. Here we get 0. Thus finding the square root of 225 by long division is completed. Therefore, 15 is the square root of 225.
Explore Square roots using illustrations and interactive examples
 Finding the square root is an inverse process of squaring the number.
 Irrational numbers cannot be expressed as a ratio of two integers. Example: π and √sqrt 2. This makes 225 is rational as it can be expressed as 225/1.
 225 is a perfect square.
Tips and Tricks
 Subtract from 225 by successive odd natural numbers, until you obtain 0. The number of times you subtract gives you the square root of 225.
 Check by the know multiplication fact that 225 = 15 × 15.
Square Root of 225 Solved Examples

Example 1: Mark wants to fence his square backyard. He knows his backyard is 225 square feet. How many feet of fencing will Mark need?
Solution:
To fence he needs to know each side of his backyard. All the sides of the fence are equal.
Area = Side × Side = 225 sq feet.
As, 15 × 15 = 225
Each side will be = 15 feetHe needs to fence 4 × 15 = 60 sq feet.

Example 2: James wants to buy a new rug for his living room. In the store he finds a square rug that has an area of 25 sq feet.
a. How long is each side of the rug?
b. How many of those rugs are needed to cover an area of 225 square feet?Solution
a. Area is 25 sq feet = side × side sq feet.
The length of each side of the rug will be 5 feet.b. To cover an area of 225 square feet, he needs 225 ÷ 5 = 45 rugs.
FAQs On Square Root of 225
How do you find the square root of 225?
The inverse operation of squaring is finding square root. 15 × 15 = 225.
Thus the inverse is √225= √(15 × 15) = 15
Is 225 a perfect cube?
225 is a perfect square and not a perfect cube. 225 = 15 × 15. 225 cannot be expressed as number × number × number(a group of 3 numbers). Thus, 225 is not a perfect cube.
Is the square root of 225 irrational?
No, the square root of 225 is not irrational as square root of 225 is 15, which is a rational number.
Is the square root of 225 a real number?
Yes, the square root of 225 is a real number.
What is square root of 225 in radical form?
The square root of 225 in the radical form denotes the positive root of 225. i.e.√225 = 15