How do you simplify $sqrt7(sqrt14 + sqrt3)$ ?

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Answer 1 · 2017-10-08T13:12:16

See a solution process below:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$sqrt( color(red)(7) ) ( sqrt(color(blue)(14)) + sqrt(color(blue)(3)) ) =>$

$(sqrt(color(red)(7)) xx sqrt(color(blue)(14))) + (sqrt(color(red)(7)) xx sqrt(color(blue)(3)))$

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

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

$sqrt(color(red)(7) xx color(blue)(14)) + sqrt(color(red)(7) xx color(blue)(3)) =>$

$sqrt(98) + sqrt(21)$

We can rewrite the term on the left as:

$sqrt(49 xx 2) + sqrt(21)$

We can use the reverse of the rule above to simplify the term on the left:

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

$sqrt(color(red)(49) xx color(blue)(2)) + sqrt(21) =>$

$(sqrt(color(red)(49)) xx sqrt(color(blue)(2))) + sqrt(21) =>$

$(7 xx sqrt(color(blue)(2))) + sqrt(21) =>$

$7sqrt(color(blue)(2)) + sqrt(21)$

How do you simplify sqrt7(sqrt14 + sqrt3)sqrt7(sqrt14 + sqrt3)?