What Is The Square Root Of 8?

Looking for the answer to the square root of 8, let me explain it in detail. The Square of a number is a number that when multiplied by itself is equal to the first number. The number 8 square root will be a number that will be the number when multiplied by itself giving you the answer 8. Let us see about the square root of 8.

What Is The Square Root Of 8?

The square root of 8 in radical form is written as √8 and the answer of squareroot of 8 is 2.82842712. It can also be expresseed as √8 = 2√2

Square Root Of 8 Simplified

√8 = 22 = 2.8284271247461903

Square Root Of 8 In Exponential Form

√8 = (8)½

Square Root Of 8 In Radical Form

√8 = √8 or 2 √2

Square Root Of 8 Cubed

√8 = 3√8

How To Find The Square Root Of 8?

To find the squareroot of 8 there are 2 methods.

Simplifying The Radical Method
Long Division Method

Let us find out the squareroot of 8 by these to methods

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Simplifying The Radical Method

First we need to see the Prime factorization of 8

8 = 2 x 2 x 2

Then it can be simplified as

√8 = √( 2 x 2 x 2)

√8 = 2√2

Now √2 = 1.414

So √8 = 2 x 1.414

√8 = 2.818

So the value of square root of 8 is 2.818

Long Division Method

The square root of 8 in long division method is done in 5 steps

Step 1

Start by pairing the numbers from right under the bar

Step 2

Take the number that squares to a number that is less than or equal to the number 8.

For number 8 2 squares to 4 and 3 squares to 9 so we will take the number 2.

Step 3

Now write number 2 as quotient as well as divisor where you will get 4 as remainder.

Step 4

Now double the number that is the divisor and write it on the left side. Here now the divisor is 2 so the number will be 4.

Step 5

Now read and understand this carefully

You have to take such the largest number that when the number is multiplied by both the digits of the divisor the answer should be less than or equal to the divisor. Here the number will be get

You have to write the remainder and repeat it to the desired decimal places.

Is the Square Root of 8 Rational or Irrational?

The Square Root of 8 is an irrational number.

A rational number is a number that can be written in p/q form also. In p/q form p and q are integers and q should not be equal to zero.

An irrational number is a number that is not a rational number.

The squareroot of 8 is 2.828427125 which is a nonterminating decimal with nonrepeating digits and 2.828427125 cannot be written in p/q form.

FAQ

What Is Square Root 8 Simplified?

The squareroot of 8 simplified is √8 = √22

First we need to see the Prime factorization of 8

8 = 2 x 2 x 2

Then it can be simplified as

√8 = √( 2 x 2 x 2)

√8 = 2√2

Now √2 = 1.414

So √8 = 2 x 1.414

√8 = 2.818

So the value of squareroot of 8 is 2.818

What Has A Square Root Of 8?

The squareroot of 8 in radical form is represented as √8 which is also equal to 2√2 and as a fraction, it is equal to 2.828 approximately.

What Is The Square Of 8?

The square of 8 is 64 and the squareroot of 8 is 2.828 or √8 = 2√2.

What Does 3 √8 Mean?

Example Cube Roots

The cube root of 8 is written as 3√8=2. The cube root of 10 is written as 3√10=2.154435.

Why √8 Is Written As 2 √2?

We need to express 8 as the product of its prime factors i.e. 8 = 2 × 2 × 2. Therefore, √8 = √2 × 2 × 2 = 2 √2. Thus, the square root of 8 in the lowest radical form is 2 √2.

Does The Square Root Of 8 Ever End?

On the other hand, rational numbers are decimals that can be written as fractions that divide two integers (as long as the denominator is not 0). Thus, for this problem, since the square root of 8, or 2.828, is a non-terminating decimal, so the square root of 8 is irrational.

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Conclusion

So 2√2 is the square root of 8 and you can calculate the root of 8 by 3 methods. If you understand the methods then it is very easy to find the square root of 8 easily.