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

• For real numbers a and b,  if a² = 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

225 can be expressed as the ratio of two integers.
As 225 can be expressed as 225 = 225/1.
Thus 225 is rational.

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 =√(5² × 3²)
• This gives, 5 × 3 = 15

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

• Square root of 144
• Square root of 169
• Square root of 400
• Square root of 288
• Square root of 900

• 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.

• 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.

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