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Square Root

What Is the Square Root of 7? | How to Find the Square Root of 7?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 7? | How to Find the Square Root of 7?

What Is the Square Root of 7? | How to Find the Square Root of 7?

The square root of 7 is 2.645. The inversion operation of addition is subtraction and the same goes for multiplication and division. Understanding a square root is as simple as that. The inversion of the square root value is squaring the given number. The square root of the number is the value when multiplied by itself gives the original number. 

For the number that are perfectly square, there are three ways to find them for the numbers that are not square use of the long division is the standard way to find them. When a number is given, a square root must be found. First, we have to check whether the number is a perfect square or not or you can also check if the number is an irrational number or not.

To know whether the number is rational or irrational. Let us take two numbers p and q if pq≠ 0 then the number is a rational number. If the two numbers p and q when divided equally to 0 then the given number is an irrational number p q ≠ 0.

Prime factorization method

Since the number 7 is an irrational number we can obtain √7 by multiplying it twice
7 = (number× number)
= 2.64× 2.64
= 7

Square root of 7 using the long division method

  • Step 1: Find the nearest integer that can divide the number
    • The nearest integer that can divide 7 is 2. 
  • Step 2: Divide the numbers until you reach a satisfactory digit after the decimal
Long division method
  • Step 3: The quotient is the square root of the number
    • 7 = 2.64

Solved example

Q1: Find the square root of 4 using the repeated subtraction method

  • 4 – 1 = 3
  • 3 – 3 = 0
    • √4 = 2

Q2: What is the square root of 7

Long division method

A2: √7 = 2.64

Q3: Louis is playing in his yard. The gate in his yard is 12 square feet. Find the height of the gate. 
A3: If we find the square root area of the gate then we can easily find the height of the gate,
Use the knowledge of square root to find the solution,
√12 = √3× √4
12 = √3 ×2 =  2√3
The side length of the gate = 2√3 feet

Q4: What is the square root of 7 using the prime factor
A4: 7 = (number ×number)
= 2.64× 2.64
= 7

Q5: What is the square root of -1
A5: -1 = i

Frequently asked questions

Which is the standard method to find the square root of an irrational number
The standard method to find the square root of an irrational number is the long division method.

What is the square root of 7
The 7 = 2.64

How to write the square root of 7 in exponential form? 
71/2 or 70.5 is the exponential way to write √7

How to write the square root of 7 in radical form?
The radical form of writing square root is √7

Can I find the square root of 7 using other methods?
Finding the square root for 7 is possible using the prime factorization method and the long division method but not by repeated subtraction because 7 is not a perfect square number.

Is 7  an irrational number?
Yes, 7 is an irrational number since the number is not equal to zero.

What are the methods to find the square root of a number?
There are three methods to find the square root of a number
Prime factorization method
Long division method
Repeated subtraction

We hope that we have answered all your queries regarding the square root of 7!

Written by

Prerit Jain

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