How do you evaluate (4+√50) - (3-√8)?

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Answer 1 · 2018-03-10T18:16:05

See a solution process below:

First, we can rewrite the expression as:

#4 + sqrt(50) - 3 + sqrt(8) =>#

#4 - 3 + sqrt(50) + sqrt(8) =>#

#1 + sqrt(50) + sqrt(8)#

Next, we can rewrite the radicals as:

#1 + sqrt(25 * 2) + sqrt(4 * 2)#

Then, we can use this rule for radicals to simplify the radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#1 + sqrt(color(red)(25) * color(blue)(2)) + sqrt(color(red)(4) * color(blue)(2)) =>#

#1 + sqrt(color(red)(25))sqrt(color(blue)(2)) + sqrt(color(red)(4))sqrt(color(blue)(2)) =>#

#1 + 5sqrt(color(blue)(2)) + 2sqrt(color(blue)(2))#

Now, we can factor out the common term to complete the evaluation:

#1 + (5 + 2)sqrt(color(blue)(2))#

#1 + 7sqrt(color(blue)(2))#