Square Root of 1000

Square Root of 1000 is approximately equal to 31.623. It is represented as √1000 or 1000^1/2. The Square Root of a number is defined as the number that when multiplied by itself gives the original number.

When multiplied by itself, √1000 will result in the number 1000. Hence, the value of the square root of 1000 is almost equal to 31.623. In this article, we will learn what is the value of the square root of 1000, how to find the value of the square root of 1000.

Square Root of 1000

Square Root of 1000 is almost equal to 31.628. As the square root of 1000 is an irrational number (non-terminating non-repeating decimal expansion), it can’t be calculated to exact decimal points.

Square Root of 1000 is given as:

31.623 ×  31.623 ≈ 1000

OR

√1000 = 31.6227766 . . .

Square Root of 1000 Calculator

How to Find the Square Root of 1000?

To find the square root, first, see if the number is a perfect square, which means its root is a whole number. It’s easier to figure out the square root of a perfect square than a number that’s not perfect. If not a perfect squre, we can use the following methods to find its value:

• Long Division Method
• Prime Factorization Method

Let’s learn about these method in detail one by one:

Square Root of 1000 by Long Division Method

To find the square root of any number using Long Division, we can use the following steps:

Step 1: Write the number in the right side of division column and group the digits of 1000 into pairs: 10 00. 00 00 . . .

Step 2: Find the largest integer whose square is less than or equal to the leftmost group (1 in this case).

Step 3: Write this integer as the quotient and divide it into 1000.

Step 4: Subtract the result from 1000, and bring down the next pair of digits (00).

Perform these stpes similar to the following illustration to find the required value upto any number of decimal palces.

Result: The result is the square root of 1000: √1000 ≈ 31.62 (rounded to two decimal place).

Square Root 1000 by Prime Factorization Method

To find the square root of 1000 using prime factorization method, follow these steps:

• Step 1: Find the Prime Factos of 1000.

Thus, Prime factors of 1000 are 2³ × 5³

• Step 2: Pair two same factors together and take one from each pair to multiply togehter to find square root of 1000.

1000 = (2 × 2) × (5 × 5) × 2 × 5

⇒ √1000 = 2 × 5 √( 2 × 5)

• Step 3: Simplify to find the value of square root of 1000,

√1000 = 10√10

Thus, the square root of 1000 by prime factorization method is 10√10.

Is Square Root 1000 an Irrational Number or Rational Number?

As we know, if the decimal representation of a number terminates or repeats, it is a rational number; otherwise, it is an irrational number. For √1000, we know that the decimal expansion is non-terminating and non-repeating. Thus, √1000 is an irrational number.

Square Root of 1000 – FAQs

What is the Value of Square Root of 1000?

The value of the square root of 1000, is 12.

Is Square Root of 1000 Rational or Irrational Number?

Square Root of 1000 i.e., √1000 is an rational number as it can be written as √1000 = 12

Is 1000 a Perfect Square?

Yes, 1000 is a perfect square as it can be written as 12 × 12

Is the Square Root of 1000 Negative?

Square root of 1000 is 12, which is an positive integer or a natural number.