Square Root Of 392 Simplified

Simplify Square Root

Here we will show you two methods that you tin employ to simplify the square root of 392. In other words, we will show y'all how to observe the square root of 392 in its simplest radical grade using two dissimilar methods.

To be more than specific, we take created an illustration beneath showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" within the radical (√) as small every bit possible.

√392 = A√B

Greatest Perfect Square Cistron Method
The Greatest Perfect Square Gene Method uses the greatest perfect square factor of 392 to simplify the square root of 392. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect foursquare from the list of all factors of 392. The factors of 392 are ane, 2, 4, 7, 8, xiv, 28, 49, 56, 98, 196, and 392. Furthermore, the greatest perfect foursquare on this list is 196 and the foursquare root of 196 is fourteen. Therefore, A equals 14.

B = Calculate 392 divided past the greatest perfect foursquare from the listing of all factors of 392. We determined above that the greatest perfect square from the listing of all factors of 392 is 196. Furthermore, 392 divided past 196 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 392 in its simplest radical form as follows:

√392 = A√B

√392 = 14√2

Double Prime Gene Method
The Double Prime Cistron Method uses the prime number factors of 392 to simplify the foursquare root of 392 to its simplest class possible. This is how to summate A and B using this method:

A = Multiply all the double prime factors (pairs) of 392 and so take the square root of that production. The prime number factors that multiply together to make 392 are 2 x ii x 2 x 7 x 7. When nosotros strip out the pairs only, we get 2 x 2 ten 7 ten 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 392 by the number (A) squared. xiv squared is 196 and 392 divided by 196 is 2. Therefore, B equals 2.

Once over again we take A and B and can get our answer to 392 in its simplest radical form as follows:

√392 = A√B

√392 = 14√2

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