Square Root of 10 is 3.16227766. It is represented as √10 or 10^1/2. Square Root of a number is the number that when multiplied by itself gives the original number which is called the Square of the Square Root number.

In this article, we will learn what is the value of the square root of 10 and how to find the value of the square root of 10.

Value of Root 10

Value of the Square Root of 10 is often called the value of root 10 which is given as follows:

Square Root of 10 = √10 = 3.16227766

In square root form, the value of the square root of 10 is given as √10 or √5√2. Since the decimal value of √5 is 2.236 and that of √2 is 1.414, the root of 10 can also be written in the decimal form as 3.1622. The extended square root of 10 is 3.16227766.

In standard cases, the square root of a number is calculated only up to three digits after decimal.

Square Root of 10 Calculator

Try out the following square root calculator to find the value of root 10

How to Find the Square Root of 10?

As mentioned, the square root of a number is a whole number that when multiplied with itself, gives the original number.

We can find the square root of 10 using the following two methods:

• Square Root 10 Value by Long Division Method

• Square Root of 10 Using Prime Factorization

Let’s learn, these methods in detail.

Square Root of 10 by Long Division Method

In the case of 10, since 10 is not a perfect square, we will have to use the long division method to find its square root. Long Division Method is the most suitable method to find the value of square root of non perfect square numbers. Follow the following steps to find the square root of 10 using the long division method:

Step 1: Write 10 as 10.000000. We will be using these zeroes for decimal division later on.

Step 2: Search for the perfect square that is less than 10. In this case, it is 9.

Step 3: To obtain 9, we will use 3 as divisor, hence, the quotient at this point is 3 and the remainder is 1.

Step 4: Put a decimal in the quotient and bring one pair of zeroes next to the remainder 1 and add 3 in the divisor.

Step 5: Now we have 6 as the new divisor and 100 as the new dividend.

Step 6: Now find a number for the unit place of divisor such that the same number can be placed in the quotient after the decimal and the resultant product of the divisor and the new number in quotient is smaller than or equal to the dividend. In this case, that number is 1 since 61 × 1 = 61 which is less than 100.

Step 7: Bring the next pair of zeroes down and repeat steps 4 and 5.

You can calculate these values upto two decimal places to get an approximate value for the square root of 10.

Learn, Square Root by Long Division Method

Square Root of 10 using Prime Factorization

When expressed as a product of its primes, 10 can be written as: 2 × 5

Hence, √10 = √(2 × 5)

When we calculate the square root of a perfect square number, we simply take one value out of the two repeated ones and multiply them to get an answer.

However, in the case of 10, we can’t pick any such pairs. Thus, the most that we can do is express the square root of 10 as √(2 × 5).

Hence, the value of square root using prime factorization is given as: √10 = √2 × √5

Now,

• √2 = 1.414..
• √ 5 = 2.236…

Hence, √10 = √(2 × 5) = 1.414.. × 2.236… = 3.162…

Also Check, Prime Factorization

Related Reads

• Square Root Formula
• List of Square Roots from 1 to 30

Square Root of 10 – FAQs

What is Value of Square Root of 10 in Decimal Form?

The value of square root of 10 in decimal form is equal to 3.16227766…

Is Square Root of 10 Rational or Irrational?

Since, the square root of 10 is 3.16227766…. We can see that it is neither terminating nor non-terminating repeating. Thus, the square root of 10 is an irrational number.

How to Write Square Root of 10?

Square Root of 10 can be written as √10.

Is 10 a Perfect Square?

No, 10 is not a perfect square because it’s prime factors – 2 × 5 can’t be paired because of a single value of 2 and 5.

Is -3.162 a Square Root of 10?

Yes, -3.162 is a square root of 10 because -3.162 × -3.162 = 9.9980 which is approximately equal to 10.

Is √2√5 Square Root of 10?

Yes, since √2√5 x √2√5 is equal to 2 × 5 = 10, it is a square root of 10.