Simplify Square Root of 7406

Here we will show you two methods that you can use to simplify the square root of 7406. In other words, we will show you how to find the square root of 7406 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√7406 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7406 to simplify the square root of 7406. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 7406. The factors of 7406 are 1, 2, 7, 14, 23, 46, 161, 322, 529, 1058, 3703, and 7406. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 7406 divided by the greatest perfect square from the list of all factors of 7406. We determined above that the greatest perfect square from the list of all factors of 7406 is 529. Furthermore, 7406 divided by 529 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 7406 in its simplest radical form as follows:

√7406 = A√B

√7406 = 23√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7406 to simplify the square root of 7406 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 7406 and then take the square root of that product. The prime factors that multiply together to make 7406 are 2 x 7 x 23 x 23. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 7406 by the number (A) squared. 23 squared is 529 and 7406 divided by 529 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 7406 in its simplest radical form as follows:

√7406 = A√B

√7406 = 23√14

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Simplify Square Root of 7407
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