Square Root

# What Is the Square Root of 64? How To Find the Square Root of 64?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Is the Square Root of 64? How To Find the Square Root of 64?

**Square Root of 64 is 8.** The square root of a number is the inversion of squaring the given numbers or when the value is multiplied by itself it gives the original value. Let us take 64 as an example. The **√**64 is 8 and by squaring 8^{2 }we get 64. The square root symbol is denoted as before going ahead with any number for finding their square root we have to check whether the given number is a perfect square number or not.

The perfect square is the number that when squared has a whole number like **√**4 = 2. The non-perfect square numbers are the ones that don’t have a square number when they are squared like **√**2 = 1.4142.

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**Rational and irrational numbers**

Rational numbers are the ones that when divided are not equal to zero let us take two values p and q, by dividing p with q, p/q NOT=0. They are usually a whole number.

For an irrational number, the remainder is not a whole number but the one with the decimal. Let us take p and q when they are divided they are not equal to zero and are not expressed as the ratio of two integers.

**How to find the square root of 64?**

The given number 64 is a perfect square, rational number. To find the square root three methods are used.

- Long division method
- Prime factorization method
- Repeated subtraction method

**Long division method**

Choose the number that when multiplied twice the result is 64. The number when multiplied twice gives 64 is 8. Hence 8 is the divisor.

Hence, the **√64 = 8.**

**Prime factorization method**

To find the square root of a number using the prime factorization method. First, find the prime factors of the given number. Let n be the factors when squaring a similar number we get n^{2} by multiplying the remaining square we get the square root of the number.

Prime factor of 64 = 2×2×2×2×2×2 or 2^{6}

Now let us take the similar squares

Now, multiply the squares 2×2×2 = 8

Hence, the **√64 = 8.**

**Repeated subtraction method**

Start to subtract the number with odd numbers. The first odd number to go is 1. Then take the result and start subtracting with the next odd number. Repeat the steps until you reach zero. The step in which zero is attained is the square root of the number.

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

The step in which zero is obtained is 8, Hence, **√64 = 8.**

**Solved examples**

**Example 1: If the area of the circle is 64𝛑 square inches find the radius of the circle.**

Area of the square =𝛑r2

𝛑r^{2} = 64𝛑

Since 𝛑 i is common we will cancel that

We get r^{2} = **√**64

r= **8 **

The radius of the circle is 8 inches.

**Example 2: Solve 2 √64 + 8√ 64**

The square root of** √64 = **8

=2 (8) + 8 (8)

= 16+64

=80

**Example 3: The class of 3rd B has 64 students if the number of students to be seated should be equal in the same row and column how many students can sit in a row.**

Total number of students = 64

When, they need to be seated equally then the number has to be equally split,

By taking the square root **√64 **we get 8

Hence, 8 people are seated equally in both row and column.

**Example 4: Robin wants to simply ****64**** to its simplest form, come let’s help her**

64 = 8 × 8

Hence the simplest form of **√64 = 8**

**Example 5: what is the value of x, if x √64 = 8**

x**√**64 = 8**√**64 = 8

Hence, x*8 = 8

X = 8/8 = 1

Therefore x = 1.

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**Frequently asked questions**

**What is the square root of 64?**

The **√**64 = 8.

**What is a perfect square number?**

A perfect square number is one when we find the root of the number we get a whole number and not a decimal. 64 = 8 hence 64 is a perfect square number.

**Is 64 a rational number?**

Yes, 64 is a rational number because when we divide the number we get 8 and not 0 (p/q 0)

**What is the square root of 121?**

The **√**121 = 11

**What is the square root of 49?**

The square root of 49 = 7.

**What are the methods to find the square root of a number?**

There are three methods to find the square root of a number

1. Prime factorization method

2. Long division method

3. Repeated subtraction

**How to find the square root for irrational numbers?**

To find the square root for irrational numbers use the long division method

Written by

Prerit Jain