SOLUTION: I do not fully understand radical expressions like 7 times the square root of 12. How exactly do you find the answer and is there a good way for me to check my answer on paper or w

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Question 422841: I do not fully understand radical expressions like 7 times the square root of 12. How exactly do you find the answer and is there a good way for me to check my answer on paper or with a calculator?
Also how do you add and subtract them to get answers with a number outside a square root like 6 times the square root of 54 or something.
One more question. When there are letters and numbers with the variable is it any different to solve. For example the square root of 128n^17

Help would be much appreciated! Im trying to learn all this without a teacher.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
I do not fully understand radical expressions like 7 times the square root of 12.
Taking your example
Factor 12 in a way the reveals at perfect square

Extract the square root of 4, which is 2
= , no further action can be taken
:
Check this on a calc: enter 7* to get 24.2487..
Then enter your solution: 14* to get 24.2487.., the same if you did it right.
:
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Also how do you add and subtract them to get answers with a number outside a square root like 6 times the square root of 54 or something.
:
You can add and subtract only like terms, For example + =
but + are not like terms and can't be added
:
However, after simplifying they may be like terms, this example
+
Factor 54 to reveal a perfect square
+
Extract the square root of 9
+ = + =
now they are like terms so we have:
:
One more question. When there are letters and numbers with the variable is it any different to solve. For example the square root of 128n^17
:
Using we can factor to reveal perfect squares

remember the sqrt of n^16 is n^8 (n^8*n^8), so we have

:
We treat variables the same way, just remember the law of exponents.