Simplify Square Root of 53290

Here we will show you two methods that you can use to simplify the square root of 53290. In other words, we will show you how to find the square root of 53290 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.

√53290 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53290 to simplify the square root of 53290. 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 53290. The factors of 53290 are 1, 2, 5, 10, 73, 146, 365, 730, 5329, 10658, 26645, and 53290. Furthermore, the greatest perfect square on this list is 5329 and the square root of 5329 is 73. Therefore, A equals 73.

B = Calculate 53290 divided by the greatest perfect square from the list of all factors of 53290. We determined above that the greatest perfect square from the list of all factors of 53290 is 5329. Furthermore, 53290 divided by 5329 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 53290 in its simplest radical form as follows:

√53290 = A√B

√53290 = 73√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53290 to simplify the square root of 53290 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 53290 and then take the square root of that product. The prime factors that multiply together to make 53290 are 2 x 5 x 73 x 73. When we strip out the pairs only, we get 73 x 73 = 5329 and the square root of 5329 is 73. Therefore, A equals 73.

B = Divide 53290 by the number (A) squared. 73 squared is 5329 and 53290 divided by 5329 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 53290 in its simplest radical form as follows:

√53290 = A√B

√53290 = 73√10

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Simplify Square Root of 53291
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