Simplify Square Root of 45253

Here we will show you two methods that you can use to simplify the square root of 45253. In other words, we will show you how to find the square root of 45253 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.

√45253 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45253 to simplify the square root of 45253. 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 45253. The factors of 45253 are 1, 13, 59, 767, 3481, and 45253. Furthermore, the greatest perfect square on this list is 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Calculate 45253 divided by the greatest perfect square from the list of all factors of 45253. We determined above that the greatest perfect square from the list of all factors of 45253 is 3481. Furthermore, 45253 divided by 3481 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 45253 in its simplest radical form as follows:

√45253 = A√B

√45253 = 59√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45253 to simplify the square root of 45253 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 45253 and then take the square root of that product. The prime factors that multiply together to make 45253 are 13 x 59 x 59. When we strip out the pairs only, we get 59 x 59 = 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Divide 45253 by the number (A) squared. 59 squared is 3481 and 45253 divided by 3481 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 45253 in its simplest radical form as follows:

√45253 = A√B

√45253 = 59√13

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Simplify Square Root of 45254
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