The square root of 8 is expressed as √8 in the radical develop and as (8)½ or (8)0.5 in the exponent create. The square root of 8 rounded as much as 8 decimal areas is 2.82842712. It is the positive solution of the equation x2 = 8. We deserve to express the square root of 8 in its lowest radical create as 2 √2.

You are watching: Square root of -1 over 8

What Is the Square Root of 8?

We know that addition has an inverse operation as subtraction and also multiplication has an inverse procedure as division. Similarly, finding the square root is an inverse procedure of squaring a number. The square root of 8 gives a number that when multiplied to itself provides the number 8. Hence, we need 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 deserve to be expressed in the form of p/q, wbelow p and q are integers and also q is not equal to 0. A number that is not a rational number is referred to as an irrational number. Non-terminating decimals that have repetitive numbers after the decimal suggest are rational numbers. Now let us look at the square root of 8. The decimal depiction 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 certainly talk about two methods to discover the square root of 8.

Simplifying the radical of the numbers that are perfect squaresLong department strategy for perfect and also non-perfect squares

The prime factorization of 8 is 8 = 2 × 2 × 2. Thus, 8 deserve to be simplified better as 8 =(2 × 2 × 2) = 22. Therefore, we have actually expressed the square root of 8 in the most basic 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 department approach is composed of the adhering to steps:

Step 1: Starting from the ideal, we will certainly pair up the digits by placing a bar over them.Step 2: Find a number that, as soon as multiplied to itself, offers the product less than or equal to 8. So, the number is 2. Keeping the divisor as 2, we gain the quotient as 2 and also the remainder as 4.Tip 3: Double the divisor and also enter it via a blank on its appropriate. Guess the largest possible digit to fill in the empty which will end up being the new digit in the quotient, such that once the new divisor is multiplied to the brand-new quotient the resultant product is less than or equal to the dividfinish. Divide and compose the remainder. Repeat this process to acquire the decimal places you desire.

See more: D&Amp;D 5E Cloak Of Protection, Risk For Vitamin D Deficiency


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

Explore square roots utilizing illustrations and also interactive examples

Important Notes:

Square root is the inverse operation of squaring.Square root of 8 have the right to be expressed as 8 = 81/2.We have the right to find the square root of 8 utilizing the radical create and the long department approach.

Think Tank:

We recognize that (-22) × (-22) = 8. So, have the right to we say that -22 is a square root of 8?Can you recognize a quadratic equation whose roots are 22 and -22?