Square Root of 0.5205 (√.5205)

Square Root of 0.5205

Here we will calculate the square root of 0.5205 (√.5205) and explain why the square root of 0.5205 is greater than 0.5205.

0.5205 can be divided into two parts. The number before and the number after the decimal point. The number before the decimal point is the whole number, and the number after the decimal point is the decimal part:

0 = Whole Number
5205 = Decimal Part

A number (x) where the whole number is not 0, is greater than the square root of the number (x):

x > √x

This makes sense because √x times √x equals x. However, this does not hold true if the whole number is 0. In that case, the opposite is true.

OK. First things first. Below is the answer to the square root of 0.5205.

√0.5205 ≈ 0.72145685941711
√0.5205 ≈ 0.72146

As you can see, 0.72146 is greater than 0.5205. Thus, two larger numbers multied together equals a smaller number! So, how is it possible that the square root of 0.5205 is greater than 0.5205?

To explain, we start by giving you a small division lesson. A division problem has a dividend, a divisor, and a quotient, like this:

dividend ÷ divisor = quotient

Looking at the division equation above, you can conclude that if the dividend increases by a larger amount than the divisor, then the quotient will increase. Furthermore, if the dividend increases by a smaller amount than the divisor, then the quotient will decrease.

1041 divided by 2000 equals 0.5205, thus we can make it into a division problem like this:

√1041 ÷ √2000 = √0.5205
1041 ÷ 2000 = 0.5205

The reason the square root of 0.5205 is greater than 0.5205 is because when you take the square root of the dividend (√1041), the decrease of the dividend is smaller than the decrease of the divisor when you take the square root of the divisor (√2000).

This would not be the case if the whole number in front of the decimal point wasn't 0.

Square Root of a Decimal
Enter another decimal number below to get the square root of it.

Square Root of 0.5206
Here is the next decimal number on our list that we calculated the square root for.