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165 LearnersLast updated on December 2nd, 2024
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
Square Root of 245 Examples
Problem 1
If, x²=245, find the value of x.
Explanation
Problem 2
Verify if √245 is greater than 15.
Explanation
Problem 3
Express the square root of 245 in the simplest radical form.
Explanation
Problem 4
Solve: 10/√245
Explanation
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?
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.
