Square Root of 256
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Last updated on August 5, 2025

The square root of 256 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 256. The number 256 has a unique non-negative square root, called the principal square root.

What Is the Square Root of 256?

The square root of 256 is ±16, where 16 is the positive solution of the equation x2 = 256. Finding the square root is just the inverse of squaring a number and hence, squaring 16 will result in 256. The square root of 256 is written as √256 in radical form, where the ‘√’  sign is called the “radical” sign. In exponential form, it is written as (256)1/2 

Finding the Square Root of 256

We can find the square root of 256 through various methods. They are:

  • Prime factorization method
  • Approximation/Estimation method
     

Square Root of 256 By Prime Factorization Method

The prime factorization of 256 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore, i.e., we first prime factorize 256 and then make pairs of two to get the square root.

So, Prime factorization of 256 =  2× 2×2×2×2×2×2×2


Square root of 256 = √[2× 2×2×2×2×2×2×2] =  2× 2×2×2 =16

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Square Root of 256 By Long Division Method

This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 256:


 Step 1: Write the number 256 and draw a bar above the pair of digits from right to left.


 Step 2: Now, find the greatest number whose square is less than or equal to 2. Here, it is 1 because 12=1 < 2


Step 3: now divide 256 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder.  Double the divisor 1, we get 2, and then the largest possible number A1=6 is chosen such that when 6 is written beside the new divisor 2, a 2-digit number is formed →26, and multiplying 6 with 26 gives 156, which
when subtracted from 156, gives 0.


Repeat this process until you reach the remainder of 0.

  Step 4: The quotient obtained is the square root of 256. In this case, it is 16.

Square Root of 256 By Subtraction Method

We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:


Step 1: Take the number 256 and then subtract the first odd number from it. Here, in this case, it is 256-1=255
Step 2: We have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 255, and again subtract the next odd number after 1, which is 3, → 255-3=252. Like this, we have to proceed further.


Step 3: Now we have to count the number of subtraction steps it takes to yield 0 finally.Here, in this case, it takes 16 steps .
            

So, the square root is equal to the count, i.e., the square root of 256 is ±16.

Common Mistakes and How to Avoid Them in the Square Root of 256

When we find the square root of 256, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.
 

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Problem 1

Find the radius of a circle whose area is 256π cm².

Okay, lets begin

 Given, the area of the circle = 256π cm2


Now, area = πr2 (r is the radius of the circle)


So, πr2 = 256π cm2


We get, r2 = 256 cm2


r = √256 cm


Putting the value of √256 in the above equation, 


We get, r = ±16 cm


Here we will consider the positive value of 16.


Therefore, the radius of the circle is 16 cm

.
Answer: 16 cm.
 

Explanation

We know that, area of a circle = πr2 (r is the radius of the circle). According to this equation, we are getting the value of “r” as 16 cm by finding the value of the square root of 256.
 

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Problem 2

Find the length of a side of a square whose area is 256 cm²

Okay, lets begin

Given, the area = 256 cm2


We know that, (side of a square)2 = area of square


Or,  (side of a square)2 = 256


Or,  (side of a square)= √256


Or, the side of a square = ± 16.


But, the length of a square is a positive quantity only, so, the length of the side is 16 cm.


Answer: 16 cm
 

Explanation

 We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its square root is the measure of the side of the square 
 

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Problem 3

Simplify the expression: √256 ╳ √256, √256+√256

Okay, lets begin

 √256 ╳ √256


 =  √(16 ╳ 16)    ╳    √(16 ╳ 16)


 =  16 ╳ 16


 =  256


√256+√256


= √(16 ╳ 16)  + √(16 ╳ 16) 


= 16 + 16


= 32


Answer: 256, 32
 

Explanation

In the first expression, we multiplied the value of the square root of 256 with itself. In the second expression, we added the value of the square root of 256 with itself.
 

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Problem 4

If y=√256, find y²

Okay, lets begin

firstly,  y=√256= 16


Now, squaring y, we get, 


y2=162=256


or, y2=256


Answer : 256
 

Explanation

squaring “y” which is same as squaring the value of √256 resulted to 256

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Problem 5

Calculate (√256/4 + √256/8)

Okay, lets begin

√256/4 + √256/8


 = 16/4 + 16/8


 = 4 + 2


 = 6


Answer : 6
 

Explanation

From the given expression, we first found the value of square root of 256 then solved by simple divisions and then simple addition.
 

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FAQs on 256 Square Root

1.What is the square root of -256?

2.Is 256 a rational number?

3.Is 256 a perfect square or a non-perfect square?

256 is a perfect square since 256 =16 2.
 

4.Is the square root of 256 a rational or irrational number?

 The square root of 256 is ±16. So, 16 is a rational number since it can be obtained by dividing two integers and can be written in the form 16/1    

5.What is the principal square root of 256?

 The principal square root of 256 is ±16, the positive value, but not -16
 

6.LCM of 256?

Important Glossaries for Square Root of 256

  • Exponential form:  An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent 
  • Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3
  • Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
  • Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 
  • Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24

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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.

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