Simplify Square Root of 42345

Here we will show you two methods that you can use to simplify the square root of 42345. In other words, we will show you how to find the square root of 42345 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.

√42345 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42345 to simplify the square root of 42345. 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 42345. The factors of 42345 are 1, 3, 5, 9, 15, 45, 941, 2823, 4705, 8469, 14115, and 42345. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 42345 divided by the greatest perfect square from the list of all factors of 42345. We determined above that the greatest perfect square from the list of all factors of 42345 is 9. Furthermore, 42345 divided by 9 is 4705, therefore B equals 4705.

Now we have A and B and can get our answer to 42345 in its simplest radical form as follows:

√42345 = A√B

√42345 = 3√4705

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42345 to simplify the square root of 42345 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 42345 and then take the square root of that product. The prime factors that multiply together to make 42345 are 3 x 3 x 5 x 941. 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 42345 by the number (A) squared. 3 squared is 9 and 42345 divided by 9 is 4705. Therefore, B equals 4705.

Once again we have A and B and can get our answer to 42345 in its simplest radical form as follows:

√42345 = A√B

√42345 = 3√4705

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Simplify Square Root of 42346
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