Square Root

# What is the square root of 4761? How to find the square root of 4761?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What is the square root of 4761? How to find the square root of 4761?

The square root of 4761 is 69. The square root of a number is the value when multiplied by itself gives the original number. The square root for the exponential form is denoted as (4761)^{1/2} or (4761)^{0.5 }the radical way of writing 4761 is expressed as √4761. Thus, they give the original number when the number is squared.

The number 4761 is a perfect square number that can be easily found. Since the square root of 4761 is 69, where 69 is a rational number the square root of 4761 can be found by three methods.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**Methods to find the square root of 4761**

There are three methods to find the square root of 4761

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

**Prime factorization method**

Prime factorization to find the square root is used to find only those numbers that are perfect squares. n is the prime factor. When the prime factors of the number are found the similar factors are squared as n^{2}. After taking a square on both sides the root with a square is canceled.

**Step 1: Find the prime factors of the given number**

Prime factors of 4761 = 3 x 3 x 23 x 23**Step 2: Take the similar factors, by multiplying them we get the square root**

4761 = 3 x 23 = 69

The exponential form can be written as,

4761 = 3^{2}x23^{2}.

Next, take square on both side

√4761 = (√3)^{2}x (√23)^{2}

√4761 = 3 x 23 = 69

Hence, the square root of √4761 = 69.

**Long division method**

Finding the square root of a perfect square number using the long division method is simple. The number that divides 4761 completely is the square root of the number. Find the nearest possible number that can divide by 4761 and continue till you reach zero.

*Long division for the square root of 4761*

Hence, √4761 = 69.

**Repeated subtraction method**

Repeated subtraction can be used to find the square root of any perfect squares. In this case, the given number is a four-digit number. Finding higher digits can be time-consuming and hard to solve.

Students can use repeated division for 2 or 3-digit numbers. Hence, long division and prime factors can be used to find the square root of higher numbers.

**Solved Examples**

**Example 1: What is the value of 64 when multiplied by 4761?****Solution:**

The square root of 64 = 8

Therefore, by multiplying 8×69 =552

Hence the value of 64 when multiplied by √4761 = 552.**Example 2: What is the area of the square whose each side is equal to 69 cm?****Solution:**

Area of the square = x^{2}

Here x= 69

Therefore, 692 = 69× 69 = 4761

Hence the are of the square with 69 cm = 4761 sq. cm**Example 3: Find the perimeter of the square if the area of the square tile is 4761.****Solution:**

The area of the square = 4761.

The side length of the tile = √area

Therefore, √4761 = 69

A square has 4 sides, by multiplying 69× 4 we get 276.

Therefore the perimeter of the tile = 276 units**Example 4: Find the square root of 4761 using the long division method.****Solution:**

Hence, √4761 = 69.

Example 5: What is the square root of 4761 using the prime factor

Solution:

Prime factors of 4761 = 3 x 3 x 23 x 23

By multiplying them we get the square root

4761 = 3 x 23 = 69

Hence, √4761 = 69

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**FAQs on the square root of 4761**

**What is the square root of 4761?**

Prime factors of 4761 = 3 x 3 x 23 x 23

By multiplying them we get the square root

The square root of √ 4761 = 69

**Is 4761 a perfect square number?**

Yes, 4761 is a perfect square number. When the square of 4761 is squared or multiplied by its root 69 it gives 4761.

**What is a rational number?**

A rational number is a real number where the denominator when divided

is, pq ≠ 0.

**What is the square root of 5?**

Hence, √5 = 2.23

**What is the square root of 36 using the long division method?**

Hence, √36 = 6

**What are the methods to find the square root of rational numbers?**

There are three methods to find the square root of 4761

Prime factorization method

Long division method

Repeated subtraction method

Written by by

Prerit Jain