Simplify Square Root of 53450

Here we will show you two methods that you can use to simplify the square root of 53450. In other words, we will show you how to find the square root of 53450 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.

√53450 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53450 to simplify the square root of 53450. 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 53450. The factors of 53450 are 1, 2, 5, 10, 25, 50, 1069, 2138, 5345, 10690, 26725, and 53450. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 53450 divided by the greatest perfect square from the list of all factors of 53450. We determined above that the greatest perfect square from the list of all factors of 53450 is 25. Furthermore, 53450 divided by 25 is 2138, therefore B equals 2138.

Now we have A and B and can get our answer to 53450 in its simplest radical form as follows:

√53450 = A√B

√53450 = 5√2138

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53450 to simplify the square root of 53450 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 53450 and then take the square root of that product. The prime factors that multiply together to make 53450 are 2 x 5 x 5 x 1069. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 53450 by the number (A) squared. 5 squared is 25 and 53450 divided by 25 is 2138. Therefore, B equals 2138.

Once again we have A and B and can get our answer to 53450 in its simplest radical form as follows:

√53450 = A√B

√53450 = 5√2138

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Simplify Square Root of 53451
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