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Square Root of 800

The square root of 800 is expressed as √800 in the radical form and as (800)^½ or (800)^0.5 in the exponent form. The square root of 800 rounded up to 7 decimal places is 28.2842712. It is the positive solution of the equation x² = 800. We can express the square root of 800 in its lowest radical form as 20 √2.

Square Root of 800: 28.284271247461902
Square Root of 800 in exponential form: (800)^½ or (800)^0.5
Square Root of 800 in radical form: √800 or 20 √2

1.	What is the Square Root of 800?
2.	Is Square Root of 800 Rational or Irrational?
3.	How to Find the Square Root of 800?
4.	Important Notes
5.	FAQs on Square Root of 800

What is the square root of 800?

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 800 can be written in multiple ways:

Radical form: √800 = 20√2
Decimal form: 28.284
Exponent form: (800)^1/2

Is Square Root of 800 Rational or Irrational?

800 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 800 is an irrational number.

How to Find the Square Root of 800?

There are only 2 ways to find the square root of 800-

Long Division Method
Prime Factorization

One can find out other methods by clicking here.

Long Division Method

The square root of 800 by long division method consists of the following steps:

Step 1: Starting from the right, we will pair up the digits 800 by putting a bar above 00 and 8 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 8. This will be 2 here, so place 2 in the quotient and the divisors place which will result in the remainder being 4.
Step 3: Drag down 00 beside the remainder, making the remainder 400. Also, add the divisor to itself and write it below. (2 + 2 = 4)
Step 4: Find a number X such that 4X × X results in a number less than or equal to 400. The number 48 works here, so fill it next to the divisor as well in the quotient.
Step 5: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding X to the divisor, the new divisor becomes 56.
Proceed in the same manner to get the decimal places you want.

Square root of 800

Therefore, the square root of 800 = 28.284.

Prime Factorization

To find the square root of 800, we shall first express it in terms of its prime factors. It can be written as 800 = 2 × 2 × 2 × 2 × 2 × 5 × 5.
Next, this can be reduced further to 800 = 2⁵ × 5².
Finally, to find the root of this from here it is very easy,
√800 = √(2⁵ × 5²) = 4 × 5√2 = 20√2 = 28.284

Therefore, the Square Root of 800 ≅ 28.284.

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Important Notes

There exists a positive and negative root of 800, 28.284 and -28.284.
There will be n/2 digits in the square root of an even number with n digits.
There will be (n+2)/2 digits in the square root of an odd number with n digits.

Solved Examples

Example 1: Jake wants to buy a new painting for his living room. In the store, he finds a square painting that has an area of 800 sq inches. How long is each side of the painting?

Solution:

To find the side of the painting, we will have to find the square root of 800. The square root is √800 = 28.28.
Hence, the side length of the painting is approximately 28 inches.
Example 2: What is the radius of a circle having an area of 800π square inches?

Solution:

The area is found using the formula of the area of a circle, which is πr². By the given information,
πr² = 800π
r² = 800
r = 28.284
Therefore, the radius of the circle is ≅ 28.3 inches.
Example: If the surface area of a cube is 4800 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 4800 in²
⇒ a = ±√800 in
Since length can't be negative,
⇒ a = √800
We know that the square root of 800 is 28.284.
⇒ a = 28.284 in

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FAQs on the Square Root of 800

What is the Value of the Square Root of 800?

The square root of 800 is 28.28427.

Why is the Square Root of 800 an Irrational Number?

Upon prime factorizing 800 i.e. 2⁵ × 5², 2 is in odd power. Therefore, the square root of 800 is irrational.

Evaluate 6 plus 19 square root 800

The given expression is 6 + 19 √800. We know that the square root of 800 is 28.284. Therefore, 6 + 19 √800 = 6 + 19 × 28.284 = 6 + 537.401 = 543.401

Is the number 800 a Perfect Square?

The prime factorization of 800 = 2⁵ × 5². Here, the prime factor 2 is not in the pair. Therefore, 800 is not a perfect square.

What is the Square Root of 800 in Simplest Radical Form?

We need to express 800 as the product of its prime factors i.e. 800 = 2 × 2 × 2 × 2 × 2 × 5 × 5. Therefore, √800 = √2 × 2 × 2 × 2 × 2 × 5 × 5 = 20 √2. Thus, the square root of 800 in the lowest radical form is 20 √2.

What is the Square of the Square Root of 800?

The square of the square root of 800 is the number 800 itself i.e. (√800)² = (800)^2/2 = 800.

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