Simplify Square Root of 70574

Here we will show you two methods that you can use to simplify the square root of 70574. In other words, we will show you how to find the square root of 70574 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.

√70574 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70574 to simplify the square root of 70574. 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 70574. The factors of 70574 are 1, 2, 7, 14, 71, 142, 497, 994, 5041, 10082, 35287, and 70574. Furthermore, the greatest perfect square on this list is 5041 and the square root of 5041 is 71. Therefore, A equals 71.

B = Calculate 70574 divided by the greatest perfect square from the list of all factors of 70574. We determined above that the greatest perfect square from the list of all factors of 70574 is 5041. Furthermore, 70574 divided by 5041 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 70574 in its simplest radical form as follows:

√70574 = A√B

√70574 = 71√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70574 to simplify the square root of 70574 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 70574 and then take the square root of that product. The prime factors that multiply together to make 70574 are 2 x 7 x 71 x 71. When we strip out the pairs only, we get 71 x 71 = 5041 and the square root of 5041 is 71. Therefore, A equals 71.

B = Divide 70574 by the number (A) squared. 71 squared is 5041 and 70574 divided by 5041 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 70574 in its simplest radical form as follows:

√70574 = A√B

√70574 = 71√14

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Simplify Square Root of 70575
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