Square Root of 0.7746 (√.7746)

Square Root of 0.7746

Here we will calculate the square root of 0.7746 (√.7746) and explain why the square root of 0.7746 is greater than 0.7746.

0.7746 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
7746 = 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 0.7746.

√0.7746 ≈ 0.880113629027525
√0.7746 ≈ 0.88011

As you can see, 0.88011 is greater than 0.7746. Thus, two larger numbers multied together equals a smaller number! So, how is it possible that the square root of 0.7746 is greater than 0.7746?

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.

3873 divided by 5000 equals 0.7746, thus we can make it into a division problem like this:

√3873 ÷ √5000 = √0.7746
3873 ÷ 5000 = 0.7746

The reason the square root of 0.7746 is greater than 0.7746 is because when you take the square root of the dividend (√3873), the decrease of the dividend is smaller than the decrease of the divisor when you take the square root of the divisor (√5000).

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

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