Square Root of 200

Value of Square Root of 200 is 14.142. The square root of 200 is represented as √200 or 200^1/2. When multiplied by itself, √200 will result in the number 200. There are two possible values of root of 200 which are 14.142... and -14.142...

In this article, we will learn the value of the square root of 200, and how to find the value of the square root of 200.

👁 Square-root-of-200

What is Square Root of 200?

Square Root of 200 up to 10 decimal places is as follows:

√200 = 14.1421356237

The value of the square root of 200 is widely accepted as 14.142. Square Root of 200 can be represented in the following two ways:

• Radical Form: √200 = 14.1421
• Fractional Exponent Form: (200)^1/2 = 14.1421

Square Root of 200 Calculator

Try out the following calculator to find the square root of 200

How to Find the Square Root of 200?

The square root of a number is the value that when multiplied by itself, results in the number taken as input. To compute the root of a number, we usually apply one of these two methods:

• Square Root by Long division Method
• Prime Factorization Method

Square Root 200 Value by Long Division Method

It is always easier to compute the square root of perfect squares. But to compute the square root of a non-perfect square, we need to perform the long division method.

To compute the square root of 200, we need to follow the steps given below:

• Step 1: Write 200 as 200.000000 to make it easier to divide
• Step 2: Now look for the perfect square less than 200 i.e. 14 and divide the number with it.
• Step 3: Now the quotient and the remainder are 1. We will place a decimal in the quotient and bring down the pair of zeroes for further division.
• Step 4: Now add the quotient with the existing divisor, this will become the digit at the tens place for our next divisor.
• Step 5: For the unit’s place, we need to find a value that can be placed at the unit place of both quotient and the divisor such that the new divisor when multiplied with the unit digit of the quotient results in the highest number less than the remainder.
• Step 6: Now bring down the next pair of zeros and repeat the steps 4th and 5th. This can be done for infinite steps as the exact value of the square root of 200 goes up to infinite decimal places. We can compute the result up to 4 decimal places as that can be used for approx. value of the square root.

👁 Square-root-of-200-using-long-division-1

Square Root 200 by Prime Factorization Method

In Prime Factorization method we find the prime factors of the given number and make pair of prime factors. Then using rule of exponent we find the square root. The square root of 200 with prime factorization method can be calculated as follows:

• Step 1: Express 200 as Product of its prime factors: 200 = 2 × 2 × 2 × 5 × 5
• Step 2: Make Pair of Prime Factors: √200 = √(2 × 2) × 2 × (5 × 5)
• Step 3: Using Rules of Exponent: √200 = 2 × 5√2 = 10√2

If we want we can later calculate it as follows:

• Since, value of root 2 = 1.414...
• Hence, √200 = 10√2 = 10(1.414) = 14.14...

Is Square Root of 200 Rational or Irrational?

The value of √200 is 14.142… value can’t be determined exactly because it can not be represented as a fraction i.e. in the form of a/b where a and b are integers and b can’t be zero. Also, its decimal expansions are non-terminating and non-repeating.

So, the square root of 200 is an irrational number.

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