What Is 8 Square Root

Square Root of viii

The square root of 8 is expressed as √8 in the radical form and as (8)^½ or (8)^0.five in the exponent form. The square root of eight rounded up to 8 decimal places is two.82842712. It is the positive solution of the equation x² = viii. Nosotros tin limited the square root of 8 in its lowest radical form as ii √ii.

Square Root of 8: 2.8284271247461903
Square Root of 8 in exponential course: (viii)^½ or (8)^0.5
Square Root of eight in radical course: √viii or two √two

ane.	What Is the Square Root of 8?
ii.	Is Square Root of 8 Rational or Irrational?
3.	How to Find the Square Root of 8?
4.	Important Notes on Foursquare Root of 8
five.	Thinking Out of the Box!
half dozen.	FAQs on Square Root of 8

What Is the Square Root of 8?

Nosotros know that addition has an changed operation as subtraction and multiplication has an inverse performance as division. Similarly, finding the square root is an inverse operation of squaring a number. The foursquare root of 8 gives a number that when multiplied to itself gives the number viii. Hence, nosotros accept to recall of a number whose square is 8.

Is the Square Root of viii Rational or Irrational?

A rational number is a number that can be expressed in the course of p/q, where p and q are integers and q is non 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. At present allow us look at the square root of eight. The decimal representation of √8 is 2.828427125

Practise you think the decimal office stops afterward 2.828427125?

No, information technology is never-ending. It is a not-terminating decimal with non-repeating digits. The number ii.828427125... tin't be written in p/q form.

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 eight.

Simplifying the radical of the numbers that are perfect squares
Long segmentation method for perfect and non-perfect squares

The prime factorization of viii is eight = 2 × 2 × 2. Therefore, √8 can be simplified further equally √8 =√(2 × two × 2) = two√2. Thus, nosotros have expressed the square root of 8 in the simplest radical form equally ii√ii

So,√8 = ii√ii

Square Root of 8 by Long Division Method

The value of the foursquare root of viii by long segmentation method consists of the following steps:

Step 1 : Starting from the correct, we volition pair up the digits by putting a bar above them.
Step ii: Find a number that, when multiplied to itself, gives the product less than or equal to viii. And so, the number is 2. Keeping the divisor equally 2, we go the quotient as 2 and the rest as iv.
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 caliber the resultant product is less than or equal to the dividend. Split up and write the remainder. Repeat this procedure to get the decimal places y'all want.

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

Explore square roots using illustrations and interactive examples

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Important Notes:

Square root is the changed operation of squaring.
Foursquare root of 8 can be expressed as √8 = 8^i/2.
Nosotros tin find the foursquare root of 8 using the radical course and the long division method.

Think Tank:

We know that (-2√2) × (-2√2) = 8. And then, tin we say that -2√2 is a square root of 8?
Tin yous make up one's mind a quadratic equation whose roots are 2√ii and -2√ii?

Example 1: Mr. Smith wants to fence his square garden. The garden has an area of 8 square feet. How long is each side of the garden?

Solution

To find the side of the square garden, we volition have to find the foursquare root of 8. The square root of 8 is √8 = ii√2. Hence, the side length of the garden is two√ii anxiety.

Case 2: Lucy is doing yoga in her yard. The gate in her g has an area of 12 foursquare feet. What is the height of the gate?
Example 2: Lucy is doing yoga in her yard. The gate in her one thousand has an area of 12 square feet. What is the height of the gate?

Solution

Past finding the foursquare root of the expanse of the gate, we can find the side length of the gate.

Using the belongings of foursquare roots, we take√12 = √3× √iv = √3× ii = 2√3

Hence, the side length of the gate is ii√3feet.
Case 3: If the area of a square is 8 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 8 in²
⇒ a = ±√eight in
Since length can't be negative,
⇒ a = √8 = two.828 in

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FAQs on the Square Root of viii

What is the Value of the Square Root of 8?

The foursquare root of 8 is ii.82842.

Why is the Foursquare Root of eight an Irrational Number?

Upon prime factorizing 8 i.e. two³, 2 is in odd ability. Therefore, the square root of 8 is irrational.

What is the Square Root of eight in Simplest Radical Class?

We need to express viii equally the production of its prime number factors i.eastward. eight = two × 2 × ii. Therefore, √8 = √two × two × 2 = 2 √2. Thus, the square root of 8 in the lowest radical form is 2 √2.

If the Square Root of eight is 2.828. Find the Value of the Foursquare Root of 0.08.

Let u.s. represent √0.08 in p/q grade i.e. √(8/100) = 0.08/10 = 0.283. Hence, the value of √0.08 = 0.283

What is the Square Root of -8?

The square root of -8 is an imaginary number. Information technology tin can be written as √-8 = √-ane × √viii = i √8 = 2.828i
where i = √-1 and it is called the imaginary unit.

Is the number viii a Perfect Square?

The prime factorization of 8 = 2³. Hither, the prime cistron ii is non in the pair. Therefore, eight is non a perfect foursquare.