Simplify Square Root of 45602

Here we will show you two methods that you can use to simplify the square root of 45602. In other words, we will show you how to find the square root of 45602 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.

√45602 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45602 to simplify the square root of 45602. 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 45602. The factors of 45602 are 1, 2, 151, 302, 22801, and 45602. Furthermore, the greatest perfect square on this list is 22801 and the square root of 22801 is 151. Therefore, A equals 151.

B = Calculate 45602 divided by the greatest perfect square from the list of all factors of 45602. We determined above that the greatest perfect square from the list of all factors of 45602 is 22801. Furthermore, 45602 divided by 22801 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 45602 in its simplest radical form as follows:

√45602 = A√B

√45602 = 151√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45602 to simplify the square root of 45602 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 45602 and then take the square root of that product. The prime factors that multiply together to make 45602 are 2 x 151 x 151. When we strip out the pairs only, we get 151 x 151 = 22801 and the square root of 22801 is 151. Therefore, A equals 151.

B = Divide 45602 by the number (A) squared. 151 squared is 22801 and 45602 divided by 22801 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 45602 in its simplest radical form as follows:

√45602 = A√B

√45602 = 151√2

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Simplify Square Root of 45603
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