Simplify Square Root of 72961

Here we will show you two methods that you can use to simplify the square root of 72961. In other words, we will show you how to find the square root of 72961 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.

√72961 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72961 to simplify the square root of 72961. 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 72961. The factors of 72961 are 1, 7, 49, 1489, 10423, and 72961. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 72961 divided by the greatest perfect square from the list of all factors of 72961. We determined above that the greatest perfect square from the list of all factors of 72961 is 49. Furthermore, 72961 divided by 49 is 1489, therefore B equals 1489.

Now we have A and B and can get our answer to 72961 in its simplest radical form as follows:

√72961 = A√B

√72961 = 7√1489

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72961 to simplify the square root of 72961 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 72961 and then take the square root of that product. The prime factors that multiply together to make 72961 are 7 x 7 x 1489. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 72961 by the number (A) squared. 7 squared is 49 and 72961 divided by 49 is 1489. Therefore, B equals 1489.

Once again we have A and B and can get our answer to 72961 in its simplest radical form as follows:

√72961 = A√B

√72961 = 7√1489

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Simplify Square Root of 72962
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