Simplify Square Root of 73458

Here we will show you two methods that you can use to simplify the square root of 73458. In other words, we will show you how to find the square root of 73458 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.

√73458 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73458 to simplify the square root of 73458. 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 73458. The factors of 73458 are 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 53, 63, 66, 77, 99, 106, 126, 154, 159, 198, 231, 318, 371, 462, 477, 583, 693, 742, 954, 1113, 1166, 1386, 1749, 2226, 3339, 3498, 4081, 5247, 6678, 8162, 10494, 12243, 24486, 36729, and 73458. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 73458 divided by the greatest perfect square from the list of all factors of 73458. We determined above that the greatest perfect square from the list of all factors of 73458 is 9. Furthermore, 73458 divided by 9 is 8162, therefore B equals 8162.

Now we have A and B and can get our answer to 73458 in its simplest radical form as follows:

√73458 = A√B

√73458 = 3√8162

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73458 to simplify the square root of 73458 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 73458 and then take the square root of that product. The prime factors that multiply together to make 73458 are 2 x 3 x 3 x 7 x 11 x 53. 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 73458 by the number (A) squared. 3 squared is 9 and 73458 divided by 9 is 8162. Therefore, B equals 8162.

Once again we have A and B and can get our answer to 73458 in its simplest radical form as follows:

√73458 = A√B

√73458 = 3√8162

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Simplify Square Root of 73459
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