Simplify Square Root of 70220

Here we will show you two methods that you can use to simplify the square root of 70220. In other words, we will show you how to find the square root of 70220 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.

√70220 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70220 to simplify the square root of 70220. 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 70220. The factors of 70220 are 1, 2, 4, 5, 10, 20, 3511, 7022, 14044, 17555, 35110, and 70220. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 70220 divided by the greatest perfect square from the list of all factors of 70220. We determined above that the greatest perfect square from the list of all factors of 70220 is 4. Furthermore, 70220 divided by 4 is 17555, therefore B equals 17555.

Now we have A and B and can get our answer to 70220 in its simplest radical form as follows:

√70220 = A√B

√70220 = 2√17555

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70220 to simplify the square root of 70220 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 70220 and then take the square root of that product. The prime factors that multiply together to make 70220 are 2 x 2 x 5 x 3511. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 70220 by the number (A) squared. 2 squared is 4 and 70220 divided by 4 is 17555. Therefore, B equals 17555.

Once again we have A and B and can get our answer to 70220 in its simplest radical form as follows:

√70220 = A√B

√70220 = 2√17555

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Simplify Square Root of 70221
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