# What Is The Square Root Of 4761?

You are here to get the answer to the question of what is the  Square Root Of 4761, let us see how it is calculated. The Square of a number is a number that when multiplied by itself is equal to the first number. The number 4761 square root will be a number which when multiplied by itself gives you the answer 4761. Let us see about the Square Root Of 4761.

## What Is The Square Root Of 4761?

The Square Root Of 4761 in radical form is written as √4761 and the answer to the square root of 4761 is  69.

• Square Root Of 4761

√4761 =  69

• Square Root Of 4761 In Exponential Form

√4761 = (4761)½

• Square Root Of 4761 In Radical Form

4761 = 4761

## How To Find The Square Root Of 4761?

To find the square root of 4761 there are 2 methods.

• Prime Factorization
• Long Division Method

Let us find out the square root of 4761 by both methods

• ### Prime Factorization

To get the answer to the square root for 4761 through the radical form method is very simple.

Now as 4761 is a prime number so

• 4761 = 3×1587
• 4761 = 3x3x529
• 4761 = 3x3x23x23

So,

• 4761 =3x3x23x23

4761 =(3×23)²

4761 =(69)²

4761 = 69

Therefore, the answer for √4761 = 69

• ### Long Division Method

The Square Root Of 4761 in long division method is done in these steps

To find the square root of 4761 using the long division method, follow these steps:

Step 1:

Write the numbers on the right side we will put a bar above it

Step 2:

Write such number on the left side that when we multiplied by itself you get a number that is either <=4761. Here you need to write 69 as the divisor and 69 as the quotient when multiplied 69 by 69 you get 4761 and the remainder will be 0.

Your quotient is 69 And your divisor is 69 and the remainder is 0 as you have got your remainder as 0 it cannot be further divided.

So the square root of 4761 is 69

## Is the Square Root Of 4761 Rational or Irrational?

The Square Root Of 4761 is a rational number.

As there is the number 69 that when multiplied by itself will give you the answer 4761 so it is a perfect square so this number is a rational number.

Also, the square root of 4761 is 69 which gives you a remainder of 0.

So 4761 is a rational number

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## FAQ

### How Do You Find The Square Root Of 4761?

You can find the square root of 4761 with the prime factorization method

4761 = 3×1587 = 3x3x529 = 3x3x23x23

So 4761 =3x3x23x23 =(3×23)² =(69)² = 69

Therefore, the answer for √4761 = 69

### Why Is The Square Root Of 4761?

The square root of 4761 is 69 which makes 4761 a perfect square as 69 x 69 is exactly 4761.

### What Is The Square Root Of 4761 With A Solution?

The solution of the square root of 4761 with the prime factorization method

4761 = 3×1587 = 3x3x529 = 3x3x23x23

So 4761 =3x3x23x23 =(3×23)² =(69)² = 69

Therefore, the answer for √4761 = 69

### Is 4761 A Perfect Square?

Yes, 4761 is a perfect square as 69 x 69 is 4761.

## Conclusion

So  69 is the Square Root Of 4761 and you can calculate the root of 4761 by 2 methods which are the prime factorization & Long Division Method. After understanding the methods mentioned above you can easily find the Square Root Of 4761.

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