Square Root of 8

The square root of 8 is ±2.82842712475, where 2.82842712475 is the positive solution of the equation x² = 8. Finding the square root is just the inverse way of squaring a number, and hence, squaring 2.82842712475 will result in 8.

The square root of 8 is written as √8 in radical form, where the ‘√’  sign is called the “radical”  sign. In exponential form, it is written as (8)^1/2.

The prime factorization of 8 can be found by dividing the 8 by prime numbers and continuing to divide the quotients until they can’t be divided anymore. After factorizing 8, make pairs out of the factors to get the square root. If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the acquired pairs.

So, Prime factorization of 8 = 2 × 2 × 2 = 2³

But here, only a pair of factor 2 can be obtained and a single 2 is remaining

So, it can be written as  √8 =  2√2.

Square root of 8 = √[2 × 2 × 2] = 2√2, i.e., 2.82842712475

This is a method, mainly used for obtaining the square root for non-perfect squares. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too, where the dividend is the number we are finding the square root of.

Follow the steps to calculate the square root of 8:

 Step 1: Place the number 8, just the same as the image, starting from right to left, and draw a bar above the pair of digits since 8 is a 1-digit number, so simply just draw a bar above 8. 

Step 2: Now, find the greatest number whose square is less than or equal to 8. Here, it is 2, because 2²=4 < 8

Step 3: Now divide 8 by 2 (the number we got from step 2) and we get a remainder. Double the divisor 2, we get 4 and find the largest possible number A, put it in the right of 4, through this, a double-digit is formed. Now multiply this with the same number A. Repeat this process until you reach the remainder of 0.

Step 4: The quotient we got is the square root. In this case, it is 2.828….

Follow the steps below: 

Step 1: find the square roots of the perfect squares above and below 8

Below : 4 → square root of 4 =2  …. (i)

Above : 9 →square root of 9 = 3 …..(ii)

Step 2: Dividing 8 with one of 2 or 3 

If we choose 3 and divide 8 by 3, we are getting 2.666 …..(iii)

Step 3:  find the average of 3 (from step (ii)) and 2.666 (from step (iii))

(3+2.666)/2 = 2.8333 

Hence, 2.8333 is the approximate square root of 8

• Exponential form: An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent.

• Factorization: Expressing the given expression as a product of its factors

• Prime Numbers: Numbers that are greater than 1, having only 2 factors as →1 and Itself. 

•   Rational numbers and Irrational numbers: The numbers that can be expressed as p/q, where p and q are integers and q is not equal to 0 are called Rational numbers. Numbers that cannot be expressed as p/q, where p and q are integers and q is not equal to 0 are called Irrational numbers. 

• Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places.  Non-perfect square numbers are those numbers whose square roots comprise decimal places.