How do you simplify $sqrt20 + sqrt45$ ?

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Answer 1 · 2018-03-20T22:12:35

See a solution process below:

First, rewrite the term under each radical as:

$sqrt(4 * 5) + sqrt(9 * 5)$

Now, use this rule for radicals to simplify each radical:

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

$sqrt(color(red)(4) * color(blue)(5)) + sqrt(color(red)(9) * color(blue)(5)) =>$

$sqrt(color(red)(4))sqrt(color(blue)(5)) + sqrt(color(red)(9))sqrt(color(blue)(5)) =>$

$color(red)(2)sqrt(color(blue)(5)) + color(red)(3)sqrt(color(blue)(5))$

Now, factor out the common term to complete the simplification:

$(color(red)(2) + color(red)(3))sqrt(color(blue)(5)) =>$

$color(red)(5)sqrt(color(blue)(5))$

How do you simplify sqrt20 + sqrt45sqrt20 + sqrt45?