228 LearnersLast updated on May 26th, 2025
Square Root of 245
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
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:
Mistake 1
Thinking 245 is a perfect square
Few students mistakenly think that 245 is a perfect square, as it lies between 15and 16. They should not rely on assuming the squares of the numbers, instead children should practice square roots of numbers and apply the methods to find square roots.
Square Root of 245 Examples
Problem 1
If, x²=245, find the value of x.
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.
Problem 2
Verify if √245 is greater than 15.
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.
Problem 3
Express the square root of 245 in the simplest radical form.
√ 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
Problem 4
Solve: 10/√245
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
FAQs on 245 Square Root
1.What is the perfect square factor of 245?
2.Is 3 divisible by 245?
3.Is √245 an irrational number?
4.Is 245 a perfect Square?
5.What is 245 divisible by?
6.How can children in Thailand use numbers in everyday life to understand Square Root of 245?
7.What are some fun ways kids in Thailand can practice Square Root of 245 with numbers?
8.What role do numbers and Square Root of 245 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Square Root of 245 skills?
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.
Explore More numbers
Previous to Square Root of 245
About BrightChamps in Thailand
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.
