Simplify Square Root of 15463

Here we will show you two methods that you can use to simplify the square root of 15463. In other words, we will show you how to find the square root of 15463 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.

√15463 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15463 to simplify the square root of 15463. 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 15463. The factors of 15463 are 1, 7, 47, 329, 2209, and 15463. Furthermore, the greatest perfect square on this list is 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Calculate 15463 divided by the greatest perfect square from the list of all factors of 15463. We determined above that the greatest perfect square from the list of all factors of 15463 is 2209. Furthermore, 15463 divided by 2209 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 15463 in its simplest radical form as follows:

√15463 = A√B

√15463 = 47√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15463 to simplify the square root of 15463 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 15463 and then take the square root of that product. The prime factors that multiply together to make 15463 are 7 x 47 x 47. When we strip out the pairs only, we get 47 x 47 = 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Divide 15463 by the number (A) squared. 47 squared is 2209 and 15463 divided by 2209 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 15463 in its simplest radical form as follows:

√15463 = A√B

√15463 = 47√7

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Simplify Square Root of 15464
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