Simplify Square Root of 2450

Here we will show you two methods that you can use to simplify the square root of 2450. In other words, we will show you how to find the square root of 2450 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.

√2450 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2450 to simplify the square root of 2450. 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 2450. The factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, and 2450. Furthermore, the greatest perfect square on this list is 1225 and the square root of 1225 is 35. Therefore, A equals 35.

B = Calculate 2450 divided by the greatest perfect square from the list of all factors of 2450. We determined above that the greatest perfect square from the list of all factors of 2450 is 1225. Furthermore, 2450 divided by 1225 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 2450 in its simplest radical form as follows:

√2450 = A√B

√2450 = 35√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2450 to simplify the square root of 2450 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 2450 and then take the square root of that product. The prime factors that multiply together to make 2450 are 2 x 5 x 5 x 7 x 7. When we strip out the pairs only, we get 5 x 5 x 7 x 7 = 1225 and the square root of 1225 is 35. Therefore, A equals 35.

B = Divide 2450 by the number (A) squared. 35 squared is 1225 and 2450 divided by 1225 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 2450 in its simplest radical form as follows:

√2450 = A√B

√2450 = 35√2

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