The square source of 8 is expressed as √8 in the radical kind and together (8)½ or (8)0.5 in the exponent form. The square root of 8 rounded as much as 8 decimal areas is 2.82842712. It is the optimistic solution of the equation x2 = 8. We have the right to express the square root of 8 in its shortest radical form as 2 √2.

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## What Is the Square root of 8?

We know that enhancement has one inverse procedure as subtraction and multiplication has actually an inverse operation as division. Similarly, recognize the square source is one inverse procedure of squaring a number. The square source of 8 gives a number that when multiplied to itself offers the number 8. Hence, we have to think the 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 kind of p/q, whereby p and q room integers and q is no equal to 0. A number the is no a rational number is called an irrational number. Non-terminating decimals that have repeated numbers after the decimal suggest are rational numbers. Now let us look at the square source of 8. The decimal depiction of **√**8 is 2.828427125

Do you think the decimal component stops ~ 2.828427125?

Hence, the square source of 8 is not a reasonable number. It is one irrational number.

## How to find the Square source of 8?

We will talk about two methods to find the square source of 8.

Simplifying the radical that the number that room perfect squaresLong department method because that perfect and also non-perfect squaresThe element factorization the 8 is 8 = 2 × 2 × 2. Therefore, **√**8 have the right to be simplified further as **√**8 =**√**(2 × 2 × 2) = 2**√**2. Thus, we have expressed the square root of 8 in the easiest radical kind as 2**√**2

So, **√**8 = 2**√**2

### Square root of 8 by Long department Method

The value of the square root of 8 by long department method is composed of the adhering to steps:

**Step 1**: beginning from the right, we will pair increase the number by placing a bar over them.

**Step 2:**Find a number that, once multiplied come itself, offers the product much less than or same to 8. So, the number is 2. Maintaining the divisor as 2, we get the quotient together 2 and the remainder together 4.

**Step 3:**Double the divisor and also enter it through a empty on that is right. Guess: v the largest possible digit to to fill in the blank which will become the brand-new digit in the quotient, such that when the brand-new divisor is multiply to the new quotient the resultant product is much less than or same to the dividend. Divide and also write the remainder. Repeat this process to acquire the decimal areas you want.

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Can you usage this technique to find the square root of 7?

**Explore square roots utilizing illustrations and interactive examples**

**Important Notes:**

**√**8 = 81/2.We can find the square source of 8 making use of the radical type and the long division method.

**Think Tank:**

**√**2) × (-2

**√**2) = 8. So, have the right to we say that -2

**√**2 is a square root of 8?Can you identify a quadratic equation whose roots space 2

**√**2 and -2

**√**2?