Simplify Square Root of 45617

Here we will show you two methods that you can use to simplify the square root of 45617. In other words, we will show you how to find the square root of 45617 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.

√45617 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45617 to simplify the square root of 45617. 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 45617. The factors of 45617 are 1, 11, 13, 29, 121, 143, 319, 377, 1573, 3509, 4147, and 45617. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 45617 divided by the greatest perfect square from the list of all factors of 45617. We determined above that the greatest perfect square from the list of all factors of 45617 is 121. Furthermore, 45617 divided by 121 is 377, therefore B equals 377.

Now we have A and B and can get our answer to 45617 in its simplest radical form as follows:

√45617 = A√B

√45617 = 11√377

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45617 to simplify the square root of 45617 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 45617 and then take the square root of that product. The prime factors that multiply together to make 45617 are 11 x 11 x 13 x 29. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 45617 by the number (A) squared. 11 squared is 121 and 45617 divided by 121 is 377. Therefore, B equals 377.

Once again we have A and B and can get our answer to 45617 in its simplest radical form as follows:

√45617 = A√B

√45617 = 11√377

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Simplify Square Root of 45618
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