Square Root of 4096

Square root of 4096 is 64 and is represented as √4096 = 64. When any positive integer or negative integer is multiplied with itself, the resultant positive integer is termed as the perfect square number and the integer that was multiplied by itself will be called the square root. Symbolically it is represented as “±z × ±z = s”, where ‘z’ is an integer and ‘s’ is the square number. It is read as z is the square root of s. A detailed explanation on square roots can be obtained from Square Root.

Note the Following:

The Square root of 4096 = √4096 where √ = radical, and 4096 is the radicand.

Exponential Form of Square root of 4096 = 4096^1/2. 

Solution for √4096 = 64

Square root of 4096 is Irrational = False

What is the Square root of 4096?

The square root of 4096 is 64. In other words, the square of 64 is 4096. i.e., ±64 × ±64 is 4096. 

How to Find the Square root of 4096?

There are three methods to find the Square root of 4096:

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

Square root of 4096 by Prime Factorisation Method

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

1. Divide 4096 by prime divisors, starting with 2.
2. Group 2 same divisors and remove 1 from the root.
3. Multiply the numbers outside the root to get the square root. 

Division for 4096 and above mentioned steps shown below;

4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 

4096 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) 

√4096 = √((2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2))

√4096 = 2 × 2 × 2 × 2 × 2 × 2

√4096 = 64

Therefore the square root of 4096 = 64.

Square root of 4096 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 4096, 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 96. The first number to be used as the next divisor (Divisor of first division multiplied by the quotient of first division)

The Division completes with zero remainder. Hence the quotient is the square root, which is 64 for 4096. 

Square root of 4096 by Repeated Subtraction Method.

When a number is subtracted repeatedly, the results can be zero or negative. 

To find the square root of a number by the repeated subtraction method, the number 4096 has to be subtracted repeatedly only by odd numbers. Again the results can be 

1. Difference = zero; Then 4096 is a perfect square. Hence the square root can be determined.
2. Difference = negative; Then 4096 is not a perfect square and it has an irrational root. 
3. Let us observe if 4096 results in zero or negative number, using the subtraction table. 

At Step 64 the difference is zero, which implies that 4096 is a perfect square number and hence 64 is its root. 

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Solved Examples

1. Find the square root of 4096 by pairing factors.

The pairs of 4096 are (1, 4096), (2, 2048), (4, 1024), (8, 512), (16, 256), (32, 128), and (64, 64). Therefore the square root of 4096 is 64 using pairing factors 64 and 64. 

2. What is the square of 64?

The square of 64 is nothing but 64 times 64 and that is 4096.