Simplify Square Root of 25350

Here we will show you two methods that you can use to simplify the square root of 25350. In other words, we will show you how to find the square root of 25350 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.

√25350 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25350 to simplify the square root of 25350. 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 25350. The factors of 25350 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 169, 195, 325, 338, 390, 507, 650, 845, 975, 1014, 1690, 1950, 2535, 4225, 5070, 8450, 12675, and 25350. Furthermore, the greatest perfect square on this list is 4225 and the square root of 4225 is 65. Therefore, A equals 65.

B = Calculate 25350 divided by the greatest perfect square from the list of all factors of 25350. We determined above that the greatest perfect square from the list of all factors of 25350 is 4225. Furthermore, 25350 divided by 4225 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 25350 in its simplest radical form as follows:

√25350 = A√B

√25350 = 65√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25350 to simplify the square root of 25350 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 25350 and then take the square root of that product. The prime factors that multiply together to make 25350 are 2 x 3 x 5 x 5 x 13 x 13. When we strip out the pairs only, we get 5 x 5 x 13 x 13 = 4225 and the square root of 4225 is 65. Therefore, A equals 65.

B = Divide 25350 by the number (A) squared. 65 squared is 4225 and 25350 divided by 4225 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 25350 in its simplest radical form as follows:

√25350 = A√B

√25350 = 65√6

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Simplify Square Root of 25351
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