Simplify Square Root of 35475

Here we will show you two methods that you can use to simplify the square root of 35475. In other words, we will show you how to find the square root of 35475 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.

√35475 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 35475 to simplify the square root of 35475. 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 35475. The factors of 35475 are 1, 3, 5, 11, 15, 25, 33, 43, 55, 75, 129, 165, 215, 275, 473, 645, 825, 1075, 1419, 2365, 3225, 7095, 11825, and 35475. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 35475 divided by the greatest perfect square from the list of all factors of 35475. We determined above that the greatest perfect square from the list of all factors of 35475 is 25. Furthermore, 35475 divided by 25 is 1419, therefore B equals 1419.

Now we have A and B and can get our answer to 35475 in its simplest radical form as follows:

√35475 = A√B

√35475 = 5√1419

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 35475 to simplify the square root of 35475 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 35475 and then take the square root of that product. The prime factors that multiply together to make 35475 are 3 x 5 x 5 x 11 x 43. 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 35475 by the number (A) squared. 5 squared is 25 and 35475 divided by 25 is 1419. Therefore, B equals 1419.

Once again we have A and B and can get our answer to 35475 in its simplest radical form as follows:

√35475 = A√B

√35475 = 5√1419

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Simplify Square Root of 35476
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