Square Root of 250
Did you know, the symbol square root is written as √ and is an integral part of mathematics. Once you understand the basics of square root finding, then you can solve any square rootrelated problem. In this lesson, you will learn about square root of 250 by long division method along with solved examples.
Let us see what the square root of 250 is.
 Square Root of 250: √250 = 15.8113
 Square of 250: 250^{2} = 62500
1.  What Is the Square Root of 250? 
2.  Is Square Root of 250 Rational or Irrational? 
3.  Tips And Tricks 
4.  How to Find the Square Root of 250? 
5.  FAQs on Square Root of 250 
6.  Important Notes 
What Is the Square Root of 250?
The square root of a number is the number that gets multiplied to itself to give the product. Square root of 250 is the value obtained after performing the operation of square root on 250.
Is the Square Root of 250 Rational or Irrational?
A number that can be expressed as a ratio of two integers, that is, p/q, q is not equal to 0 is called a rational number. Now let us look at the square root of 250.
250 cannot be broken into two such factors which on squaring gives 250. It can be approximately written as a square of 15.81, which is a nonrecurring and nonterminating decimal number. This shows it isn't a perfect square which also proves that the square root of 250 is an irrational number.
Tips and Tricks:
 If 250 was a perfect square, the square root of 250 would be a rational number. This concludes that square root of any number "n," which is not a perfect square, will always be an irrational number.
How to Find the Square Root of 250?
There are different ways to calculate the square root of 250. Square root of 250 is found using the following steps:
 Step 1: Check whether the number is a perfect square or not. 250 is not a perfect square as it cannot be broken down into a product of two same numbers.
 Step 2: Once the number is checked, the following are the processes required to be followed:
 If the number is a perfect square, it can be written in this format √x^{2} = x .
 If the number is not a perfect square, the square root is found using the long division method. It can also be written in its simplified radical form of the square root.
Simplified Radical Form of Square Root of 250
The prime factorization of 250 is given as:
√250 = √10 × 25. 25 is a perfect square of 5. Hence, the square root of 25 is 5. 10 is not a perfect square, hence it remains within roots. √250 = 5√10. Simplified radical form of square root of 250 is 5√10. Let us now try finding the square root of 250 by the long division method!
Square Root of 250 by Long Division Method
Let us understand the process of finding square root of 250 by long division.
 Step 1: Pair the digits of the number from one's digit by placing a bar over them.
 Step 2: The first pair just consists of 1 number, i.e., 2. Square of 1 gives a product less than 2. The number is subtracted from the first pair and subsequently, the next pair is added as the divisor, i.e., 50.
 Step 3: The double of 1 is 2. Now a number is to be placed along with 2, i.e., 5. The product of 25 by 5 gives 125. When the difference between150 and125 is taken, the obtained value is 25.
 Step 4: Now double of the quotient is taken, i.e., 30. Now a decimal is added to the quotient, hence letting us add a pair of zeros to the original dividend. A number along with 30 is added in the blank and it is multiplied by the same number in the quotient. Product of 308 with 8 gives 2464.
 Step 5: The difference obtained from the above step is 36. The double of quotient, i.e., 316 is taken which makes the divisor 158 along with the involvement of 8. The product of 3161 with 1 gives 3161. The difference between 3600 and 3161 is 439.
 Step 6: The process is repeated the same way.
Explore square roots using illustrations and interactive examples
Important Notes:
 The square root is the inverse operation of squaring.
 Square root of 250 can be expressed as √250 or (250)^{1/2}.
 We can find the square root of 250 or any other number using the radical form and the long division method.
Square Root of 250 Solved Examples

Example 1: Is square root of 250 equal to 10 times square root of 25?
Solution
250 can be expressed as √250 = √10 × 25 = 5√10. Square root of 25 gives 5. 10 times square root of 25 is 10 × √25 = 50. Hence, square root of 250 is not equal to 10 times square root of 25.

Example 2: James wants to buy a new rug for his living room. In the store, he finds a square rug that has an area of 250 sq feet. How long is each side of the rug?
Solution
The area of one rug is 250 square feet. And we know that, area of square = (side)^{2}.
That means the length of each side of the rug is the square root of its area.
The square root of 250 is 5√10.Hence, the length of each side of the rug is 15.81 feet.
FAQs on Square Root of 250
What is the square root of 250 simplified?
We can simplify it by pulling out the number which is multiplied to itself. This gives √250 = 5 × √(2 × 5) = 5√10. Therefore the square root of 250 simplified is √250 = 5√10.
What is the square root of 250?
The square root of 250 is 5√10 or approximately 15.81139.
Is square root of 250 rational or irrational?
Since 250 is not a perfect square, and therefore it is an irrational number.
How do you find the square root of 250?
We can find the square root of 250 using the long division method.
Is square root of 250 a real number?
Yes, the square root of 250 is a real number.