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Square Root of 2000

The square root of 2000 is expressed as √2000 in the radical form and as (2000)½ or (2000)0.5 in the exponent form. The square root of 2000 rounded up to 10 decimal places is 44.7213595500. It is the positive solution of the equation x2 = 2000. We can express the square root of 2000 in its lowest radical form as 20 √5.

  • Square Root of 2000: 44.721359549995796
  • Square Root of 2000 in exponential form: (2000)½ or (2000)0.5
  • Square Root of 2000 in radical form: √2000 or 20 √5
1. What is the Square Root of 2000?
2. Is Square Root of 2000 Rational or Irrational?
3. How to Find the Square Root of 2000?
4. Challenging Questions
5. FAQs on Square Root of 2000

What is the square root of 2000?

A number when squared or multiplied by itself results in the original number n is the square root of a number n which is written as √n. The square root of 2000 can be written in multiple ways:

  • Radical form: √2000 = 20√5
  • Decimal form: 44.721
  • Exponent form: (2000)1/2

Is Square Root of 2000 Rational or Irrational?

  • 2000 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 2000 is an irrational number.

How to Find the Square Root of 2000?

There are only 2 ways to find the square root of 2000:

  • Long Division Method
  • Prime Factorization

One can find out other methods by clicking here.

Long Division Method

The square root of 2000 by long division method consists of the following steps:

  • Step 1: Starting from the right, we will pair up the digits 2000 by putting a bar above 00 and 20 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 20. This will be 4 here, so place 4 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 as (4 + 4 = 8).
  • Step 4:  Find a number X such that 8X × X results in a number less than or equal to 400. The number 84 works here, so fill 4 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 88. 
    Proceed in the same manner to get the decimal places you want.

Square root of 2000

Therefore, the square root of 2000 = 44.721.

Prime Factorization

  • To find the square root of 2000, we shall first express it in terms of its prime factors. Prime factorization of 2000 is 2000 = 2 × 2 × 2 × 2 × 5 × 5 × 5.
  • Next, this can be reduced further to 2000 = 24 × 53.
  • Finally, to find the root of this from here it is very easy,
    √2000 = √(24 × 53)  = 4 × 5√5  = 20√5 = 44.721

Therefore, the square root of 2000 ≅ 44.721.

Explore Square roots using illustrations and interactive examples

Challenging Questions

  • What is the square root of 2000 up to 6 decimal places(Use Long Division).
  • What are the roots of -2000? Also, find the value of the square of the negative root of (-√(2000))2?
 

Solved Examples

  1. Example 1: Justin wants to buy a new painting for his living room. In the store, he finds a square painting that has an area of 2000 sq inches. What is the perimeter of the painting? Round your answer to the nearest whole number.

    Solution:

    To find the side of the painting, we will have to find the square root of 2000. The square root is √2000 = 44.72. Hence, the side length of the painting is approximately 45 inches.

  2. Example 2: What is the perpendicular length in between two circles having an area of 2000π and 3000π inches square respectively? Round your answer to the nearest tenth.

    Solution:

    The area is found using the formula of the area of a circle, which is πr2. By the given information,
    A1 = πr12 = 2000π
    A2 = πr22 = 3000π
    We need to find the distance r2 - r1. 
    r12 = 2000 and r22 = 3000
    r1 = √2000 and r2 = √3000 = √(1.5 × 2000)
    So, r2 - r1 = √(1.5 × 2000) - √2000 = √2000 × (√1.5 - 1) = 44.721 × 0.2247 = 44.496.

    Therefore, the distance between the circles is 44.5 inches.

  3. Example: If the area of a circle is 2000π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 2000π in2
    ⇒ r = ±√2000 in
    Since radius can't be negative,
    ⇒ r = √2000
    The square root of 2000 is 44.721.
    ⇒ r = 44.721 in

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FAQs on the Square Root of 2000

What is the Value of the Square Root of 2000?

The square root of 2000 is 44.72135.

Why is the Square Root of 2000 an Irrational Number?

Upon prime factorizing 2000 i.e. 24 × 53, 5 is in odd power. Therefore, the square root of 2000 is irrational.

Is the number 2000 a Perfect Square?

The prime factorization of 2000 = 24 × 53. Here, the prime factor 5 is not in the pair. Therefore, 2000 is not a perfect square.

What is the Square Root of -2000?

The square root of -2000 is an imaginary number. It can be written as √-2000 = √-1 × √2000 = i √2000 = 44.721i
where i = √-1 and it is called the imaginary unit.

What is the Value of 4 square root 2000?

The square root of 2000 is 44.721. Therefore, 4 √2000 = 4 × 44.721 = 178.885.

What is the Square of the Square Root of 2000?

The square of the square root of 2000 is the number 2000 itself i.e. (√2000)2 = (2000)2/2 = 2000.

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