Square Root of 245
2026-02-28 06:09 Diff
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Last updated on August 5, 2025

A square root is a number that, when we double it, it gives you another number. It is a very important and interesting part of mathematics. You must have applied it for measuring each side of a square from the total area.

What is the Square Root of 245?

The square root of 245 is a number, when we multiply it by itself we get 245. The square root of 245 is an irrational number. As it cannot be written as a ratio of two numbers. It is denoted by 245 and is approximately equal to 15.6525. 


Exponential form : 2451/2  ≅ 15.6525.
Radical Form: √245 

Finding the Square Root of 245

We can find the square root of a number by using methods like: Prime Factorization; Long Division method; Approximation method and Subtraction method:
 

Prime Factorization

The factoring of a number into smaller numbers is prime factorization. Here, 245 is a composite number, it can be broken down into smaller numbers more than 2.


√245 = √5×7×7 = 5x72


Taking out the perfect square,


√245  =√ 5x7x7 = 7√5 =15.6525


 So, from this method we cannot find the exact square root, but we confirm that 245 is not a perfect square

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Long Division Method

In this method, we get to find the value of the square root precisely.

Grouping the digits: We start with pairing the digits from the decimal part 245.00


Find the number whose square will be less than or equal to 245 i.e., 152=225


Subtract 152=225 from 245, which leaves us with 20.


Now we bring down two zeros, which makes it 2000


Next double the divisor 15, we get 30. Next we find the largest digit which will be lesser than or equal to 2000.


Repeat the steps to get the next decimal places.

So after calculation we get, √245 = 15.6525

Approximation Method

As 152 =225 and 162 =256, the square root of 245 lies between 15 and 16.


Start by guessing 15.62 which is nearest to 15.


15.62  = 243.36 which too less


Go to the next number 15.7, 15.72 = 246.49 which is too high.


So, √245  = 15.6525

Subtraction Method

The subtraction method includes subtracting consecutive odd numbers from 245 to see how many steps we need to reach zero. However, since 245 is not a perfect square, we cannot exactly reach 0. 

245 -1 =244


244-3=241


241-5=236

As we did not get zero, we understand that 245 is not a perfect square.
 

Common Mistakes and How to Avoid Them in the Square Root of 245

While learning about square roots, students may likely make mistakes, to avoid them a few mistakes with solutions are given below:
 

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Problem 1

If, x²=245, find the value of x.

Okay, lets begin

If, x2=245


Then, 


x= √245 

Explanation

 Here, the square when shifted to the RHS it becomes the square root of the number


x=√ 5x7x7 


x=7√5


So the value of x is 7√5.

Well explained 👍

Problem 2

Verify if √245 is greater than 15.

Okay, lets begin

First, approximate √245 :


Using prime factorization:


√245 = √5x49 = 7√5


Since 5 = 2.236


7√5 = 7 × 2.236 =15.652


Since 15.652>15, we conclude that : 


√245 > 15

Explanation

The approximation of  √245 shows us that it is greater than 15.

Well explained 👍

Problem 3

Express the square root of 245 in the simplest radical form.

Okay, lets begin

√ 245  = 5 × 72


We use the square root property:


√245 = √5x7x7 


Now take out the square of the number which is 7×7 = 49, take out 7.


√245 = 7√5 


So, the value is  7√5 .

Explanation

The square root of 245 in the simplest form is 7√5

Well explained 👍

Problem 4

Solve: 10/√245

Okay, lets begin

 To simplify, 10/ √245  We multiply the number in the denominator with the numerator and the denominator, which is called rationalizing. 

Explanation

10/ √245  /x  √245 / √245  = 10√245 / 245  , here when two square roots with the same number are multiplied the roots get canceled (in the denominator), and we are left with the same number, hence √245 x √245  = 245.
After rationalizing, we get,  10 x √245 /245 

Well explained 👍

FAQs on 245 Square Root

1.What is the perfect square factor of 245?

To find the perfect square of a number, we multiply the number by itself. 245 is not a perfect square but to make it a perfect square, the least number that should be multiplied is 5.
 

2.Is 3 divisible by 245?

The sum of the digits of 245, 2+4+5=11. As 11 is not divisible by 3. No, 245 is not divisible by 3.
 

3.Is √245 an irrational number?

Yes, √245 is an irrational number, as it cannot be written in p/q form, √245  =√245 /1 where p is not an integer.

4.Is 245 a perfect Square?

No, 245 is not a perfect square. It cannot be written as two equal numbers.
 

5.What is 245 divisible by?

The numbers 1,5,7,35,49,245 divide 245.
 

Important Glossaries for Square Root of 245

  • Irrational number: A number that cannot be written in the form of a ratio or fraction. For example, √245 is an irrational number.
  • Exponent form: Writing the square root of a number in the form of degree or powers. For example, 2451/2  ≅ 4.7958
  • Square root: It is a number that, when we double it, it gives you another number. For example, 4 × 4 =16.
     

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.