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How do you multiply #sqrt2(3sqrt14 - sqrt7)#?

Answer 1

Eva Abramson

#6sqrt7-sqrt14#

Multiply #sqrt2# by each term in the parentheses

#sqrt2(3sqrt14-sqrt7)#

#sqrt2*3sqrt14-sqrt2*sqrt7#

#3sqrt28-sqrt14 rarr 3sqrt28# can be simplified

#3sqrt28=3sqrt4*sqrt7 rarr# #4# is a perfect square

#6*sqrt7=6sqrt7=3sqrt28#

#6sqrt7-sqrt14#

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Answer 2

Ethan Adkins

To multiply sqrt2(3sqrt14 - sqrt7), you can use the distributive property. Multiply sqrt2 by each term inside the parentheses separately.

sqrt2 * 3sqrt14 = 3sqrt(214) = 3sqrt28 = 6sqrt7 sqrt2 * -sqrt7 = -sqrt(27) = -sqrt14

Therefore, the result of multiplying sqrt2(3sqrt14 - sqrt7) is 6sqrt7 - sqrt14.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.