Square Root of 64

Square Root of 64 is 8. Square Root is the value that provides an original number by multiplying with itself. If the square root asks, in the situation “What number, when multiplied by itself, gives 64?” It is the inverse action of squaring. “The square root of 64 is 8”. Although, if the answer is 8 and -8, we usually consider the positive root. However, both 8 and -8 are square roots of 64.

In this article, we will learn what we are the roots of 64, how to find the value of the square root of 64 using different methods.

What is Square Root of 64?

Square root of 64, is denoted as √64 and it’s equal to 8. So, the original positive number is ‘8’ multiplied by itself 8 × 8 then we get the number 64. Square Root of 64 is represented as follows:

√64 = 8

(64)^1/2 = 8

Square Root Calculator

Try out the following calculator to calculate the square root of 64

How to Calculate Square Root of 64?

Some of the methods are given below to find out the square root of 64.

Square Root of 64 by Long Division Method

Square Root of 64 by Repeated Subtraction Method

Square Root 64 by Estimation Method

Square Root of 64 by Prime Factorization

Square Root of 64 by Long Division Method

The long division method to calculate a number’s square root requires using of a methodical approach to determining the number’s root. So, Let’s Calculate the square root of 64 by the long division method involves the following steps:

Let’s begin with the given number, and write 64.

Take the number’s digits from the right in pairs. Thus, the whole number is selected as a pair.

After that, It is necessary to divide 64 by a number so that there multiplier number is just equal to 64 or a number less than that.

Let’s try with different numbers, such as 5 × 5 = 25, 6 × 6 = 36, 7 × 7 = 49, 8 × 8 = 64.

Consequently, 8 should be the divisor, resulting in 8 as the matching quotient.

So, the multiples numbers are 8 × 8 which gives 64, which is exactly equal to the dividend.

At last, the quotient is 8, and the remainder is 0.

Learn, Square Root by Long Division Method

Square Root of 64 by Repeated Subtraction Method

The square root can be found by repeatedly subtracting odd numbers from the provided number until it equals zero. This process is known as repeated subtraction. So, In this process number of odd numbers we subtract here will be treated as a square root of 64;

64 – 1 = 63
63 – 3 = 60
60 – 5 = 55
55 – 7 = 48
48 – 9 = 39
39 – 11 = 28
28 – 13 = 15
15 -15 = 0

Therefore, The square root of 64 is 8 because we have started from 64 and subtracted with odd numbers,8 times to obtain 0.

Square Root 64 by Estimation Method

To get closer to the real value, we first estimate the square root of 64 using the estimation method. Some of the steps are given below;

Let’s take the number smaller than 64, To find the next perfect square which is 49 (49/7 squared).

But as we know, 64 has a square root of more than 7, and 64 is greater than 49.

To refine the estimate, consider that 8 squared is 64. Therefore, the square root of 64 is 8.

So consequently, that says using estimation can quickly determine the square root of 64 in between two numbers 7 and 8, and a more precise estimation is 8.

Square Root of 64 by Prime Factorization

In this method, we have to divide the given number with a prime number, beginning with 2 but if the numbers can’t be divided by 2 anymore then use the other prime number. Do it same until you get 1 at last.

64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

So Finally, we get the number 1 in the division method and here the calculation ends.

Therefore, the prime factorization of 64 is written as a product, 2 × 2 × 2 × 2 × 2 × 2 or 2⁶

Learn, Prime Factorization Method

Is Square Root of 64 Rational or Irrational?

8 is square root of 64, or √64. Since 64 may be written as the square of the integer 8, it is a perfect square in this instance (8 × 8 = 64). The square root of 64 is a rational number as 8 is an integer. In this case, the square root of 64 i.e. 8, be expressed as the fraction 8/1, that is why it square root of 64 is 8.

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Square Root of 64 Value – FAQs

What is Square Root Value of 64?

The square root of 64 is 8.

What is Square of 8?

The square of 8 can be written as 8^2 and it can be calculated as 8^2 = 8 × 8 = 64. Therefore, the square of 8 is equal to 64.

How do you Find the value of Root 64?

We can find the square root of 64 is find in many ways, like; Long division method, repeated Subtraction Method, Prime factorization and other methods.

Does a Square Root Have Two Values?

Yes, there are typically two values for a square root: a positive value and a negative one. For instance, there are two solutions for the square root of 64: +8 and -8.