Simplify Square Root of 69475

Here we will show you two methods that you can use to simplify the square root of 69475. In other words, we will show you how to find the square root of 69475 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.

√69475 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69475 to simplify the square root of 69475. 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 69475. The factors of 69475 are 1, 5, 7, 25, 35, 175, 397, 1985, 2779, 9925, 13895, and 69475. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 69475 divided by the greatest perfect square from the list of all factors of 69475. We determined above that the greatest perfect square from the list of all factors of 69475 is 25. Furthermore, 69475 divided by 25 is 2779, therefore B equals 2779.

Now we have A and B and can get our answer to 69475 in its simplest radical form as follows:

√69475 = A√B

√69475 = 5√2779

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69475 to simplify the square root of 69475 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 69475 and then take the square root of that product. The prime factors that multiply together to make 69475 are 5 x 5 x 7 x 397. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 69475 by the number (A) squared. 5 squared is 25 and 69475 divided by 25 is 2779. Therefore, B equals 2779.

Once again we have A and B and can get our answer to 69475 in its simplest radical form as follows:

√69475 = A√B

√69475 = 5√2779

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Simplify Square Root of 69476
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