The square root of 8 is expressed as √8 in the radical form and as (8)½ or (8)0.5 in the exponent form. The square root of 8 rounded up to 8 decimal places is 2.82842712. It is the positive solution of the equation x2 = 8. We can express the square root of 8 in its lowest radical form as 2 √2.

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What Is the Square Root of 8?


We know that addition has an inverse operation as subtraction and multiplication has an inverse operation as division. Similarly, finding the square root is an inverse operation of squaring a number. The square root of 8 gives a number that when multiplied to itself gives the number 8. Hence, we have to think of a number whose square is 8.


Is the Square Root of 8 Rational or Irrational?


A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. A number that is not a rational number is called an irrational number. Non-terminating decimals that have repeated numbers after the decimal point are rational numbers. Now let us look at the square root of 8. The decimal representation of 8 is 2.828427125

Do you think the decimal part stops after 2.828427125?

Hence, the square root of 8 is not a rational number. It is an irrational number.


How to Find the Square Root of 8?


We will discuss two methods to find the square root of 8.

Simplifying the radical of the numbers that are perfect squaresLong division method for perfect and non-perfect squares

The prime factorization of 8 is 8 = 2 × 2 × 2. Therefore, 8 can be simplified further as 8 =(2 × 2 × 2) = 22. Thus, we have expressed the square root of 8 in the simplest radical form as 22

So, 8 = 22

Square Root of 8 by Long Division Method


The value of the square root of 8 by long division method consists of the following steps:

Step 1: Starting from the right, we will pair up the digits by putting a bar above them.Step 2: Find a number that, when multiplied to itself, gives the product less than or equal to 8. So, the number is 2. Keeping the divisor as 2, we get the quotient as 2 and the remainder as 4.Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill in the blank which will become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the resultant product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want.

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Can you use this method to find the square root of 7?

Explore square roots using illustrations and interactive examples

Important Notes:

Square root is the inverse operation of squaring.Square root of 8 can be expressed as 8 = 81/2.We can find the square root of 8 using the radical form and the long division method.

Think Tank:

We know that (-22) × (-22) = 8. So, can we say that -22 is a square root of 8?Can you determine a quadratic equation whose roots are 22 and -22?