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Square Root

How to find the square root of 256? What is the square root of 256?

Written by Prerit Jain

Updated on: 12 Aug 2023

How to find the square root of 256? What is the square root of 256?

How to find the square root of 256? What is the square root of 256?

The square root of 256 is 16. The square root of any number is just the inversion of squaring the given number. The number when multiplied twice gives the original value.

For the given number 256, when the number 16 is squared 162 or when multiplied twice by 16×16 we get 256. For a perfect square number like 256 finding the square root of the number is simple as they are whole numbers and not integers.

Long division is used to find the square root of irrational and non-perfect square numbers. Since 256 can be the ratio of two numbers it is a rational number
p/q, q = 0.
There are three methods that are used to find the square root of a number that has perfect squares,

  • Long division method
  • Repeated subtraction method
  • Prime factorization method

Long division method

  • Step 1: Find the smallest integer that can divide the number. 
    256 is not a perfect root number and 16 is the nearest number that can divide it. 
  • Step 2: Keep following the long division using divisor and dividend. 
Long division method for the square root of 256
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.
  • Hence, √256 = 16.

Repeated subtraction method

Using the repeated subtraction method, the square root of the number can be easily solved but consumes time. Hence, the prime factorization and the long division method are widely used to find the square root of the number. Start subtracting the given number by the first odd number, take the given value, and further subtract the number with the next odd number repeat the step until you reach zero. 

Step 1256-1255
Step 2255-3252
Step 3252-5247
Step 4247-7240
Step 5240-9231
Step 6231-11220
Step 7220-13207
Step 8207-15192
Step 9192-17175
Step 10175-19156
Step 11156-21135
Step 12135-23112
Step 13112-2587
Step 1487-2760
Step 1560-2931
Step 1631-310
Table for repeated subtraction method of square root 256

Prime factorization method

Prime factorization is one of the simplest methods used to find the square root of a given number. Take the prime factor of the number as n square the given number we get n2, take a single value, and multiply with the other square. By doing so we will get the square root of the number.

  • Step 1: Find the prime factor for the given number
    256 = 2×2×2×2×2×2×2×2
  • Step 2: Pair the prime factors.
    256 = (2×2)(2×2)(2×2)(2×2)
    Take square on both sides
    √256=√2×√2×√2×√2
    You can cancel the square with the square root we get
    √256 = 2×2×2×2
  • Step 3: Multiply the factors
    The √256 = 2×2×2×2
    √256 = 16

Solved Examples

Example 1: What is the sum of the square of 256 and the square root of 256?
Solution:
Square of 256= 65,536
The square root of √256 = 16
The sum of the square of 256 and the square root of 256 = 65,536+16 = 65,552

Example 2: Joel wants to find the square root value of 4/256 to help him solve the sum
Solution:
The √256 = 16.
The √4 = 2
Therefore, the √4/256 = 2/16 = 1/8.

Example 3: Solve √256 + 2 √256
Solution:
The √256 = 16.
Hence 16 + 2 (16).
= 16+32
=48.

Example 4: What is the area of the square whose each side is equal to 16 cm
Solution:
Area of the square = x2
Here x= 16
Therefore, 162 = 16×16 = 256
Hence the area of the square with 16 cm = 256 sq. cm.

FAQs on the square root of 256

What is the square root of 256?

The square root of 256 = 16.

Explain why the square root of 256 is a rational number

When finding the prime factor of 256 we get 162 which is entirely an even power and hence all the numbers are positive integers which makes them rational numbers.

What is the value of 256 and the square root of 256?

The square root of √256 is 16, therefore 256√256 = 256×16 = 4,096

What is the real value for the square root of 256?

The actual value for the √256 = 16

What is the square root of 5?

The square root of 5 = 2.23

What is the square root of (-256)?

The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.

Is 256 a perfect square number?

Yes, 256 is a perfect square number.

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Prerit Jain

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