Simplify Square Root of 66603

Here we will show you two methods that you can use to simplify the square root of 66603. In other words, we will show you how to find the square root of 66603 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.

√66603 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66603 to simplify the square root of 66603. 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 66603. The factors of 66603 are 1, 3, 149, 447, 22201, and 66603. Furthermore, the greatest perfect square on this list is 22201 and the square root of 22201 is 149. Therefore, A equals 149.

B = Calculate 66603 divided by the greatest perfect square from the list of all factors of 66603. We determined above that the greatest perfect square from the list of all factors of 66603 is 22201. Furthermore, 66603 divided by 22201 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 66603 in its simplest radical form as follows:

√66603 = A√B

√66603 = 149√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66603 to simplify the square root of 66603 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 66603 and then take the square root of that product. The prime factors that multiply together to make 66603 are 3 x 149 x 149. When we strip out the pairs only, we get 149 x 149 = 22201 and the square root of 22201 is 149. Therefore, A equals 149.

B = Divide 66603 by the number (A) squared. 149 squared is 22201 and 66603 divided by 22201 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 66603 in its simplest radical form as follows:

√66603 = A√B

√66603 = 149√3

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