What is square root of 6 divided by square root of 77? (√6/√77)

Square root of 6 divided by square root of 77

What is the square root of 6 divided by the square root of 77? We start by displaying the problem we are solving in mathematical terms as follows:

√6 ÷ √77 =

		√6
		√77

Looking at the problem above, you see that both the numerator and the denominator have a radical (√). It is tempting to conclude that the radicals even each other out, and that you can simply divide 7 by 8 to get the answer. However, that will not give you the correct answer unless the numbers are the same.

Here we will show you two different methods you can use to calculate the square root of 6 divided by the square root of 77.

Method 1
This is the most obvious method, where you simply first calculate the square root of each number, and then divide the result, like this:

		√6
		√77

≈

		2.4494897
		8.7749644

		2.4494897
		8.7749644

≈ 0.27915

Method 2
This is our favorite method, because it is easier and faster to enter into a handheld calculator. Since √6/√77 is the same as √(7/8), you can first divide the numbers, and then find the square root of the quotient, like this:

√6 ÷ √77 ≈ √0.0779221

√0.0779221 ≈ 0.27915

As we said, we like this method because it is easy to enter into a calculator. This is what you enter into a calculator to get the answer to square root of 6 divided by square root of 77.

[6] [÷] [7] [7] [=] [√x]

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