How do you combine #\sqrt { 6} + \sqrt { 50} - \sqrt { 2}#?

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Answer 1 · 2018-01-10T11:33:16

See a solution process below:

We can rewrite the radicals as:

#sqrt(2 xx 3) + sqrt(2 xx 25) + sqrt(2 xx 1)#

Next, we can use this rule for radicals to rewrite the radicals again:

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

#sqrt(2)sqrt(3) + sqrt(2)sqrt(25) + sqrt(2)sqrt(1)#

#sqrt(2)sqrt(3) + 5sqrt(2) + 1sqrt(2)#

We can now factor out the common term giving:

#sqrt(2)(sqrt(3) + 5 + 1)#

#sqrt(2)(sqrt(3) + 6)#