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A worked example of simplifying an expression that is a sum of several radicals. In this example, we simplify √(2x²)+4√8+3√(2x²)+√8. Created by Sal Khan and Monterey Institute for Technology and Education.

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• at 2;40, why would x squared really be the absolute value of x?
• any number - either positive or negative - squared will always be positive -> therefore it will always be the absolute value of the number
• How did you know right off that they are asking for the principal square root? Is every square root aksing for the principal square root? What would be an alternative? What would it look like?
• The principle square root is simply the radical sign.
The NEGATIVE square root will have "-" before the radical sign.
If the problem wants both, it will have a "±" before the radical sign.
• I am not really sure where to put this, or find it ,but I was wondering if there are any lessons about dividing radicals?
• Dividing by a radical? While you could leave an expression in the form a/sqrt(b), it is more appropriate to multiply that by sqrt(b)/sqrt(b) to get (a*sqrt(b))/b. (This works since a number divided by itself is 1.
• At wouldn't 4lxl*√2 + 10√ = 4lxl+11√2 (meaning wouldn't the 10√2 + √2 =11√2
• Not quite, because 4|x| is multiplied by √2, not added. If it was 4|x| + √2 + 10√2, you would be correct. If you are trying to factor out the √2, you have to add together the ENTIRE numbers being multiplied by √2. So you would add 10 and 4|x|. Since these are not like terms, you get:

(4|x| + 10) * √2
• is it possible that there can be a zero or a 1 behind the radical?
• Yes, but if 1 is under the square root sign, it just simplifies to 1 because the square root of 1 is 1. For zero, the square root of zero is zero so the whole term becomes zero.
• why does Sal say at "principal square root"
• Because the √ means principal square root, not square root.
• At the answer was: (4lxl+10)√2.

• if you have a denominator that is a whole number , and the numerator is a square root, what do you do?