Simplify Square Root of 61464

Here we will show you two methods that you can use to simplify the square root of 61464. In other words, we will show you how to find the square root of 61464 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.

√61464 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 61464 to simplify the square root of 61464. 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 61464. The factors of 61464 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 197, 312, 394, 591, 788, 1182, 1576, 2364, 2561, 4728, 5122, 7683, 10244, 15366, 20488, 30732, and 61464. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 61464 divided by the greatest perfect square from the list of all factors of 61464. We determined above that the greatest perfect square from the list of all factors of 61464 is 4. Furthermore, 61464 divided by 4 is 15366, therefore B equals 15366.

Now we have A and B and can get our answer to 61464 in its simplest radical form as follows:

√61464 = A√B

√61464 = 2√15366

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 61464 to simplify the square root of 61464 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 61464 and then take the square root of that product. The prime factors that multiply together to make 61464 are 2 x 2 x 2 x 3 x 13 x 197. 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 61464 by the number (A) squared. 2 squared is 4 and 61464 divided by 4 is 15366. Therefore, B equals 15366.

Once again we have A and B and can get our answer to 61464 in its simplest radical form as follows:

√61464 = A√B

√61464 = 2√15366

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Simplify Square Root of 61465
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