199 LearnersLast updated on May 26th, 2025
Square Root of 250
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 250?
The square root of 250 is a number, when we multiply it by itself we get 250. The square root of 250 is an irrational number. As it cannot be written as a ratio of two numbers. It is denoted by 250 and is approximately equal to 15.8114.
Exponential form : 2501/2 ≅ 15.8114.
Radical Form: √250
Finding the Square Root of 250
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, 250 is a composite number, it can be broken down into smaller numbers more than 2.
250 = 2×5×5×5 = 2×53
Taking out the perfect square,
√250 = √25x10 = 5√10
So, from this method we cannot find the exact square root, but we confirm that 250 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 250.00
Find the number whose square will be less than or equal to 250 i.e., 152=225
Subtract 152=225 from 250, which leaves us with 25.
Now we bring down two zeros, which makes it 2500
Next double the divisor 15, we get 30. Next we find the largest digit which will be lesser than or equal to 2500.
Repeat the steps to get the next decimal places.
So after calculation we get, √250 = 15.8114
Approximation Method
As 152 =225 and 162 =256, the square root of 250 lies between 15 and 16.
Start by guessing 15.62 which is nearest to 15.
15.82 = 249.64 which too less
Go to the next number 15.7, 15.822 = 250.27 which is too high.
So, 250 = 15.811
Subtraction Method
The subtraction method includes subtracting consecutive odd numbers from 250 to see how many steps we need to reach zero. However, since 250 is not a perfect square, we cannot exactly reach 0.
250 -1 =249
249-3=246
246-5=241
As we did not get zero, we understand that 250 is not a perfect square.
Common Mistakes and How to Avoid Them in the Square Root of 250
While learning about Square root, students are likely to make mistakes. Below-mentioned are a few mistakes with solutions on how to avoid them:
Mistake 1
Thinking 250 is a perfect square
Few students think mistakenly that 250 is a perfect square, as it lies between 15 and 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 250 Examples
Problem 1
If, x²=250, find the value of x.
If, x2=250
Then,
x= 250
Explanation
Here is the square when shifted to the RHS it becomes the square root of the number
x= 577
x=75
So the value of x is 75.
Problem 2
Verify if √250 is greater than 15.
First, approximate √250 :
Using prime factorization:
√250 = √5x49 = 7√5
Since √5 = 2.236
7√5 = 7 × 2.236 =15.652
Since 15.652>15, we conclude that :
√250 > 15
Explanation
The approximation of √250 shows us that it is greater than 15.
Problem 3
Express the square root of 250 in the simplest radical form.
√250 = 5 × 72
We use the square root property:
√250 =√5x7x7
Now take out the square of the number which is 7×7 = 49, take out 7.
√250 = 7√5
So, the value is 7√5 .
Explanation
Square root in terms of radical form is 7√5
Problem 4
Solve: 20/√250
To simplify, 20/ √250 , we multiply the number in the denominator with the numerator and the denominator, which is called rationalizing.
Explanation
20/√250 x √250 / √250 = 20√250 /√250 , 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√ 250 x √250 = 250.
After rationalizing, we get, 20 √250 / 250
Problem 5
Simplify √25+√250
√25+√250 here we have a root inside a root, which is called a nested root.
Explanation: We first find the square root of the number that is inside, √250 =15.811
=√ 25+15.811
Now we add both the numbers. We get,
= √40.811 , next we find the square root of 40.811
= 6.39
Explanation
Answer: = 6.39
FAQs on 250 Square Root
1.Is 250 a perfect square root?
2.What are the factors of 250?
3.What is the value of √250 the nearest whole number?
4.What perfect Squares go into 250?
5.What is 250 a perfect cube?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 250?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 250?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Square Root of 250
- Irrational number: A number that cannot be written in the form of a ratio or fraction. For example, √250 is an irrational number.
- Exponent form: Writing the square root of a number in the form of degree or powers. For example, 2501/2 ≅ 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.
