Algebra: Chapter 11, Lesson 6, page 504.
Addition and Subtraction of Radical Expressions
To add and subtract radical expressions, you can use the same distributive property we have used in the past. You may have to rationalize the denominator and after that, you might be able to factor and combine expressions.
Follow along:
`sqrt(3) + sqrt((1/3)) = sqrt(3) + sqrt(1)/sqrt(3)`
now we have to rationalize the second term, by multiplying by `1/1` or `sqrt(3)/sqrt(3)`
= `sqrt(3) + sqrt(1)/sqrt(3) * sqrt(3)/sqrt(3)`, and we remember (see the denominator) that `sqrt(3)*sqrt(3) = 3`
= `1sqrt(3) + 1[sqrt(3)]/3` remember too, that 1+ 1/3 = 4/3,
then finally we have our solution = `4/3 sqrt(3)`
The best way is to see some more examples, click here for them!
Here again is a great link from Purplemath.
Two of tonight’s homework problems solved by MrE are here! Just click it.
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Algebra 1a: Chapter 9, Lesson 3, page 411.
Equations and Absolute Value
To solve an equation of the form `| A | = b`, solve the disjunction `A = b` OR `A = −b`. You will have 2 equations to solve with the right side of the second equation having the opposite sign of the first equation’s right side.
REMEMBER by definition, the solution of `| A | ≠ a` NEGATIVE NUMBER! So … the solution to these type of problems is the NULL SET! or the symbol `∅` !
Two of tonight’s homework problems solved by MrE are here! Just click it!