This is a step by step guide for finding the value of **square root of 4096**. For finding the square root of any number we have two methods. We can find square root by prime factorization method or by long division method. Generally prime factorization is used for finding square roots of small numbers. Suppose if we want to find square root for big numbers then we have solve it by long division method. Now let’s see how to find the **square root of 4096** by two methods. After seeing this answers whatever method you are feeling easy you can follow that method.

**Square root of 4096 by prime factorization method:**

Write 4096 as a product some prime numbers.

4096 = __2 × ____2__ __2 ×____ 2__ __2 × ____ 2__ __2 × ____ 2____2 × ____ 2____2 ×____ 2__

Now for each pair of 2 write one 2 and multiply it for getting square root

= 2 × 2 × 2 × 2 × 2 × 2

= 64

4096 square root is 64.

**Square root of 4096 by long division method:**

Steps:

Draw the two vertical lines.

In between write the number 4096.

From left hand side for every two digits keep the bar as shown in fig.

Now take first two digits i.e. 40.

Check that below 40 is there any perfect square number or not.

We can take 6 × 6 = 36

Subtract 36 from 40 you will get the remainder 4.

Carry down 96 down.

It becomes 496 now.

Double the quotient now.

So 2 × 6 = 12.

Write 12 below the divisor 6 and opposite to 496.

Now after 12 in the circle we have to write some number.

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The same number we have to write in the circle which is after 6 in the quotient.

Now write 4 in the circle.

It becomes 124 × 4 = 496.

As the remainder becomes “0” the quotient is the answer.

Therefore, 4096 square root is 64.

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