Simplify Square Root of 62541

Here we will show you two methods that you can use to simplify the square root of 62541. In other words, we will show you how to find the square root of 62541 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.

√62541 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 62541 to simplify the square root of 62541. 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 62541. The factors of 62541 are 1, 3, 9, 6949, 20847, and 62541. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 62541 divided by the greatest perfect square from the list of all factors of 62541. We determined above that the greatest perfect square from the list of all factors of 62541 is 9. Furthermore, 62541 divided by 9 is 6949, therefore B equals 6949.

Now we have A and B and can get our answer to 62541 in its simplest radical form as follows:

√62541 = A√B

√62541 = 3√6949

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 62541 to simplify the square root of 62541 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 62541 and then take the square root of that product. The prime factors that multiply together to make 62541 are 3 x 3 x 6949. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 62541 by the number (A) squared. 3 squared is 9 and 62541 divided by 9 is 6949. Therefore, B equals 6949.

Once again we have A and B and can get our answer to 62541 in its simplest radical form as follows:

√62541 = A√B

√62541 = 3√6949

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Simplify Square Root of 62542
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