Simplify Square Root of 37503




Here we will show you two methods that you can use to simplify the square root of 37503. In other words, we will show you how to find the square root of 37503 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.

37503 = A√B




Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37503 to simplify the square root of 37503. 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 37503. The factors of 37503 are 1, 3, 9, 27, 81, 463, 1389, 4167, 12501, and 37503. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 37503 divided by the greatest perfect square from the list of all factors of 37503. We determined above that the greatest perfect square from the list of all factors of 37503 is 81. Furthermore, 37503 divided by 81 is 463, therefore B equals 463.

Now we have A and B and can get our answer to 37503 in its simplest radical form as follows:

37503 = A√B

37503 = 9√463




Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37503 to simplify the square root of 37503 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 37503 and then take the square root of that product. The prime factors that multiply together to make 37503 are 3 x 3 x 3 x 3 x 463. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 37503 by the number (A) squared. 9 squared is 81 and 37503 divided by 81 is 463. Therefore, B equals 463.

Once again we have A and B and can get our answer to 37503 in its simplest radical form as follows:

37503 = A√B

37503 = 9√463



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