Square Root of 200

Did you know Ancient Greeks introduced the idea that the square root of positive whole numbers which are not perfect squares are irrational numbers? The square root of 200 is one such number that is irrational. In this chapter, we will calculate the square root of 200 by long division method along with solved examples.
Let us see what the square root of 200 is.

• Square Root of 200: √200 = 14.14213
• Square of 200: 200² = 40000

The square root of 200 is the value which is obtained after taking the square root of 200.

It is not possible to find such a whole number which on squaring gives 200. It can be approximately written as a square of 14.142, which is a non-recurring and non-terminating decimal number. This shows it isn't a perfect square which also proves that the square root of 200 is an irrational number.

The square root of 200 is found using the following steps:

• Check whether the number is a perfect square or not. 200 is not a perfect square as it cannot be broken down into a product of two same numbers.
• If the number is a perfect square, it can be written in this format √x² = x.
• If the number is not a perfect square, the square root is found using the long division method. It can also be written in its simplified radical form of the square root.
• In this case, 200 is not a perfect square, hence its square root is found using the long division method. The simplified radical form of the square root of 200 is given below.

Simplified Radical Form of Square Root of 200 

200 can be written as a product 2 and 100. It is given as:

√200 = √2×10²

2 is not a perfect square, hence it remains within roots. Hence, the square root of 200 in radical form is simplified as 10√2 .

Square Root of 200 by Long Division Method

The value of the square root of 200 by the long division method consists of the following steps: 

• Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
• Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 200. So, the number is 14. Putting the divisor as 14, we get the quotient as 14 and the remainder 200 - 196 = 4.
• Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want.

Hence, √200 = 14.142

Explore Square roots using illustrations and interactive examples

• Square Root of 225
• Square Root of 288
• Square Root of 256
• Square Root of 192
• Square Root of 400

Challenging Questions:

• How will Hailey find the square root of 200 using the long division method up to 3 decimal places?
• How will Billy express the square root of 200 in its simplified radical form?

Tips and Tricks:

• 200 is not a perfect square, hence its square root is an irrational number. This concludes that the square root of any number "n", which is not a perfect square will always be an irrational number.

What is the simplified version of the square root of 200?

The square root of 200 in the simplest form is 10√2.

What is 200 the square root of?

200 is the square root of 40000.

Is 200 a perfect square?

No, 200 is not a perfect square. 

Can the square root of 200 be simplified?

The square root of 200 can be simplified as 10√2.

Is the square root of 200 rational or irrational?

The square root of 200 is irrational.

Is square root of 200 a real number?

Yes, the square root of 200 is a real number.