Simplify Square Root of 74606

Here we will show you two methods that you can use to simplify the square root of 74606. In other words, we will show you how to find the square root of 74606 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.

√74606 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74606 to simplify the square root of 74606. 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 74606. The factors of 74606 are 1, 2, 7, 14, 73, 146, 511, 1022, 5329, 10658, 37303, and 74606. Furthermore, the greatest perfect square on this list is 5329 and the square root of 5329 is 73. Therefore, A equals 73.

B = Calculate 74606 divided by the greatest perfect square from the list of all factors of 74606. We determined above that the greatest perfect square from the list of all factors of 74606 is 5329. Furthermore, 74606 divided by 5329 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 74606 in its simplest radical form as follows:

√74606 = A√B

√74606 = 73√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74606 to simplify the square root of 74606 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 74606 and then take the square root of that product. The prime factors that multiply together to make 74606 are 2 x 7 x 73 x 73. When we strip out the pairs only, we get 73 x 73 = 5329 and the square root of 5329 is 73. Therefore, A equals 73.

B = Divide 74606 by the number (A) squared. 73 squared is 5329 and 74606 divided by 5329 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 74606 in its simplest radical form as follows:

√74606 = A√B

√74606 = 73√14

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Simplify Square Root of 74607
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