Simplify Square Root of 21249

Here we will show you two methods that you can use to simplify the square root of 21249. In other words, we will show you how to find the square root of 21249 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.

√21249 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21249 to simplify the square root of 21249. 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 21249. The factors of 21249 are 1, 3, 9, 27, 787, 2361, 7083, and 21249. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 21249 divided by the greatest perfect square from the list of all factors of 21249. We determined above that the greatest perfect square from the list of all factors of 21249 is 9. Furthermore, 21249 divided by 9 is 2361, therefore B equals 2361.

Now we have A and B and can get our answer to 21249 in its simplest radical form as follows:

√21249 = A√B

√21249 = 3√2361

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21249 to simplify the square root of 21249 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 21249 and then take the square root of that product. The prime factors that multiply together to make 21249 are 3 x 3 x 3 x 787. 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 21249 by the number (A) squared. 3 squared is 9 and 21249 divided by 9 is 2361. Therefore, B equals 2361.

Once again we have A and B and can get our answer to 21249 in its simplest radical form as follows:

√21249 = A√B

√21249 = 3√2361

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Simplify Square Root of 21250
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