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Last updated on September 18th, 2024
The square root of 8 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 8. The number 8 has a unique non-negative square root, known as the principal square root.
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