Square Root

# What Is The Square Root of 10? How To Find The Square Root of 10?

Written by Prerit Jain

Updated on: 17 Aug 2023

Contents

### What Is The Square Root of 10? How To Find The Square Root of 10?

**Square Root of 10:** When we multiply the number by itself we get the square root of the number or the square number. It depends on the number for which the square root needs to be found.

When the number 2 is squared 2^{2} = 4

When 6 is squared 6^{2} = 36

The **√**4 = 2.

The **√**36 = 6.

Before jumping straight into finding the square root of any number we must find whether the given number is a perfect square number or not. The numbers that end with 2,3,7 and 8 are considered perfect square numbers, and the numbers that end with 1,4,5,6, and 9 are not perfect square numbers.

As you can see there is no number mentioned above that ends with zero. This makes finding the square root of 10 a complicated one. The square root of 10 can be found using two methods replacing the unit values using unit places or by the long division method. The square root is denoted using the symbol **√** also called radix or radical symbol.

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**How to find square root of 10?**

To find the square root of a number we first go for prime factors since the number 10 doesn’t have any prime factors, so we can take the factors.

The factors of 10 are 1,2,5 and 10.

Let us now write the factors of 10 as

10 = 2*5

Since there is no square root let us take square root on both sides

**√**10 = **√**2***√**5

The root of 10 = 1.414*2.236

10 = ±3.162

**Long division method**

The nearest integer of the number is used to carry out the long division method. The number 3 is the nearest integer that can be used. Start dividing and stop when you reach a satisfactory digit.

**√10 = 3.162**

**Solved examples**

**Example 1: What is the square root of 10 using the long division method?**

**√10 = 3.162**

**Example 2: What are the factors of 10**

The factors of 10 are 1,2,5 and 10

**Example 3: What is the square root of 121 using the prime factorization method?****√**121 = 11*11

Hence, the **√**121 = 11

**Example 4: What is the square root of 2 using the long division method?**

**√2 = 1.4142**

**Example 5: what is the square root of 6 √36 + 1√10 help Raj solve the equation**

= 6 (6) + 1 (3.162)

= 36+3.162

= 39.162

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**Frequently asked question**

**Is √10 a rational number?**

No,

**√10**is an irrational number because when divided it is not equal to zero.

**What is the value of √10 ?**

The

**3.162**

**√**10 =**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 write the square root of 10 in radical form?**

The radical form of writing square root is** √10**

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

The **√**5 = 2.2360

**Which method is used to find the √10?**

The standard method that is used to find the square root of any number is the long division method.

**What is the √49?**

The

**√**49 = 7

Written by

Prerit Jain