Square root of 64 – value, derivation and examples

We know that 64 is a perfect square of 8 because 8, when multiplied by itself, gives 64. Also, we must tell you that 64 is a rational number. So, bring your square root of numbers notes as in this article, we will find how to calculate the square root of 64 and solve some examples of the same. 

Let’s get started.

Square root of 64

8 is the square root of 64 because 8 x 8 gives 64. Hence, if we inverse this operation, we get √64 = 8. The value of the square root of 64, i.e., 8 can be positive or negative. In this article, we will only consider the positive value of root 64. 

How to find the square root of 64?

There are many different methods to find the value of √64. Since we know that it is a perfect square number, we can find its square root using the prime factorisation method. 

64 is a composite number. Its factors are 1, 2, 4, 8, 16, 32, and 64.

Let us first find the prime factors of 64.

Upon factorisation, we get 64 = 2 x 2 x 2 x 2 x 2 x 2. 

So, √64 = √(2 x 2 x 2 x 2 x 2 x 2)

The factors include three pairs of number 2; therefore, we can consider each pair as one number to do away with the square root.

√64 = 2 x 2 x 2 

√64 = 8

Furthermore, 64 is a perfect square and 8 x 8 = 64. So, we can also find the root of 64 by another method, i.e., by inversing the squaring operation. 

√64 = √8²

= 8^2*(1/2) 

= 8

So, √64 is 8. 

Let us look at the root in correlation with power.

Consider the number’ a’ and a natural number ‘x.’ 

Then, a^x = a * a * a …… (multiplied ‘x’ number of times)

If the value of ‘x’ is 2 and ‘a’ is 4, then 42 = 4 x 4 = 16

This means, ‘4 raised to the power 2’ is 16.

Now, the root is the inverse of power. Therefore, we can also see that 8, when multiplied by itself, gives 64. Hence, if 64 is the square of 8 then 8 is the value of root 16.

Is the √64 rational or irrational?

If a number terminates at some point or has a repeating pattern in its decimal part. Then it can be represented as a fraction with a non zero denominator. Such numbers are rational numbers. Here, we can see that the value of √64 is 8, i.e., a whole number. So, it is a rational number. 

Facts worth considering

• 64 is itself a rational number because It can be represented in the form of p/q. Where p and q are integers and q is not equal to 0.
• The value of √64 can be calculated by the prime factorisation method because it is a perfect square. 

Examples

1. Find the dimensions of a square piece of paper if its area is equal to 64cm2.

Given, area of square = 64 cm²

Let us assume that the side of square = x cm

So, 

64 = x2 (area of square = side²)

√64 = x

8 cm = x

Therefore, the side of the square is 8 cm.

2. Simplify – √64 + 2√3

Given, √64 + 2√3

We know that √64 = 8 and √3 = 1.732

We get 

= 8 + 2(1.732)

= 8 + 3.464

= 11.464