How To Add Fractions With Radicals

in order to add or subtractterms containing radicals, the radical factorsmust be exactly the same. so for our first example we have 7 square root of 5- 3 square root 5. these are like radicalsbecause they both contain

How To Add Fractions With Radicals, a factor of square root of 5. but in general,to add or subtract radicals, we should first simplifyeach radical then identify the like radicals

and then we can add or subtractthe like radicals by adding or subtractingthe coefficients. so again for 7 square root 5- 3 square root of 5, it's importantthat we first recognize the square root of 5does not simplify because it does not containany perfect square factors and since 7 - 3 is equal to 4, 7 square root 5- 3 square root of 5 is equal to 4 square root of 5.

another way to show this would be to factor out thecommon factor of square root 5. so we factored outsquare root of 5 and put it on the right here. notice how we'd be left with7 - 3 x the square root of 5 which would give us4 square root of 5. we normally don't show itthis way but we could. next we have square rootm plus 13 square root m. it's always helpfulto have a coefficient

so this first radicalwould have a coefficient of 1, next the square root of mdoes not simplify because it does not containany perfect square factors. notice both terms do containa factor of square root m so the index is the sameand the radicand is the same. so these are like radicalsand since 1 + 13 is equal to 14, 1 square root m + 13 square rootm is equal to 14 square root m. and for our last example, notice how each term containsa factor of square root of 10

and the square root of 10does not simplify. so we have 3 like radicals again because the indexesare all 2 and the radicands are all 10. and since 4 - 19 is equal to-15, and -15 + 7 is equal to -8, this simplifies to-8 square root of 10. so noticehow in all of these problems when adding or subtractinglike radicals,

the radical partdoes not change. okay, next we'll look atsome examples where we have to simplify first before we add or subtractlike radicals. i hope you found this helpful.