Simplify Square Root of 69649

Here we will show you two methods that you can use to simplify the square root of 69649. In other words, we will show you how to find the square root of 69649 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.

√69649 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69649 to simplify the square root of 69649. 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 69649. The factors of 69649 are 1, 17, 241, 289, 4097, and 69649. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 69649 divided by the greatest perfect square from the list of all factors of 69649. We determined above that the greatest perfect square from the list of all factors of 69649 is 289. Furthermore, 69649 divided by 289 is 241, therefore B equals 241.

Now we have A and B and can get our answer to 69649 in its simplest radical form as follows:

√69649 = A√B

√69649 = 17√241

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69649 to simplify the square root of 69649 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 69649 and then take the square root of that product. The prime factors that multiply together to make 69649 are 17 x 17 x 241. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 69649 by the number (A) squared. 17 squared is 289 and 69649 divided by 289 is 241. Therefore, B equals 241.

Once again we have A and B and can get our answer to 69649 in its simplest radical form as follows:

√69649 = A√B

√69649 = 17√241

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Simplify Square Root of 69650
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