Simplify Square Root of 35301

Here we will show you two methods that you can use to simplify the square root of 35301. In other words, we will show you how to find the square root of 35301 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.

√35301 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 35301 to simplify the square root of 35301. 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 35301. The factors of 35301 are 1, 3, 7, 21, 41, 123, 287, 861, 1681, 5043, 11767, and 35301. Furthermore, the greatest perfect square on this list is 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Calculate 35301 divided by the greatest perfect square from the list of all factors of 35301. We determined above that the greatest perfect square from the list of all factors of 35301 is 1681. Furthermore, 35301 divided by 1681 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 35301 in its simplest radical form as follows:

√35301 = A√B

√35301 = 41√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 35301 to simplify the square root of 35301 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 35301 and then take the square root of that product. The prime factors that multiply together to make 35301 are 3 x 7 x 41 x 41. When we strip out the pairs only, we get 41 x 41 = 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Divide 35301 by the number (A) squared. 41 squared is 1681 and 35301 divided by 1681 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 35301 in its simplest radical form as follows:

√35301 = A√B

√35301 = 41√21

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Simplify Square Root of 35302
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