Square Root of 256

Square root of 256 is 16 and is represented as √256 = 16. Square number is a positive integer that is obtained by multiplying an integer with itself. Here 256 is a perfect square number as it is obtained by multiplying 16 with 16. 256 can also be obtained by multiplying -16 with itself. Hence a square root of a positive integer can be either positive or negative. i.e., ± i × ± i = 256, where ± i is the square root of 256. The value of ± i can be obtained using the prime factorisation method, long division method, simplified method and repeated subtraction method. 

Note the Following:

The Square root of 256 = √256 where √ = radical, and 256 is the radicand.

Exponential Form of Square root of 256 = 256^1/2

Solution for √256 = 16

Square root of 256 is Irrational = False

For the detailed explanation on square roots can be obtained from Square Root.

What is the Square root of 256?

The square root of 256 is 16. In other words, the square of 16 is 256. i.e., ±16 × ±16 is 256. 

How to Find the Square root of 256?

There are three methods to find the Square root of 256:

• Prime Factorisation method
• Long Division method
• Repeated Subtraction method

Square root of 256 by Prime Factorisation Method

In the Prime Factorisation method, the following steps are performed;

1. Divide 256 by prime divisors
2. Group same two prime number and remove 1 from the root
3. Product of the number outside the root forms the square root of 256.

Above steps for 256 will be expressed as;

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

256 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)

√256 = √((2 × 2) × (2 × 2) × (2 × 2) × (2 × 2))

√256 = 2 × 2 × 2 × 2

√256 = 16

Therefore the square root of 256 = 16.

Square root of 256 by Long Division Method

In the long division method, the given numbers are paired in groups, starting from the right side. Let us understand the long division method, in detailed steps;

Step 1:  Grouping the given number into pairs

Given, number is 256. Grouping it as 2 and 56.

Step 2: Consider the first number.

Let us find a square number that divides the first number

i.e 1 × 1 = 1 

2 × 2 = 4 

3 × 3 = 9.

Step 3: Continue the division using the next number, 56. The first number to be used as the next divisor (Divisor of first division multiplied by the quotient of first division)

Since the Division is complete with the remainder as zero, the quotient becomes the square root of the given number. 

Therefore the Square root of 256 is 16.

Square root of 256 by Repeated Subtraction Method.

In the repeated subtraction method, the number 256 is subtracted repeatedly by odd numbers. There are two possibilities

1. Difference becomes zero at some point: Then, the number 256 is a perfect square and the step number is the square root of 256.
2. Difference becomes negative: Then the number 256 is not a perfect square and it does not have a rational root. 

For the given number 256, steps for repeated subtraction are

Step 16 leads to the difference zero, which implies that 256 is a perfect square number and hence 16 is its root.

Video Lessons

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Solved Examples

1. Find the square root of 256 by pairing factors.

The pairs of 256 are (1, 256), (2, 128), (4, 64), (8, 32) and (16, 16)

Therefore, the square root of 256 is 16 using pairing factors 16 and 16. 

2. What is the square of 16?

The square of 16 is nothing but 16 times 16 and that is 256.