Simplify Square Root of 1305

Here we will show you two methods that you can use to simplify the square root of 1305. In other words, we will show you how to find the square root of 1305 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.

√1305 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 1305 to simplify the square root of 1305. 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 1305. The factors of 1305 are 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, and 1305. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 1305 divided by the greatest perfect square from the list of all factors of 1305. We determined above that the greatest perfect square from the list of all factors of 1305 is 9. Furthermore, 1305 divided by 9 is 145, therefore B equals 145.

Now we have A and B and can get our answer to 1305 in its simplest radical form as follows:

√1305 = A√B

√1305 = 3√145

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 1305 to simplify the square root of 1305 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 1305 and then take the square root of that product. The prime factors that multiply together to make 1305 are 3 x 3 x 5 x 29. 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 1305 by the number (A) squared. 3 squared is 9 and 1305 divided by 9 is 145. Therefore, B equals 145.

Once again we have A and B and can get our answer to 1305 in its simplest radical form as follows:

√1305 = A√B

√1305 = 3√145

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Simplify Square Root of 1306
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