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How do you simplify #(12sqrt5-7sqrt7)+(6sqrt5-7sqrt7)#?

Answer 1

Julia Adams

#18sqrt5-14sqrt7#

Since the parenthesis are not required, we have

#color(purple)(12sqrt5)color(steelblue)(-7sqrt7)+color(purple)(6sqrt5)color(steelblue)(-7sqrt7)#

After that, we can mix similar terms to obtain

#18sqrt5-14sqrt7#

We are done because our radicals contain no perfect squares!

I hope this is useful.

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Answer 2

Eva Adamson

To simplify the expression (12√5 - 7√7) + (6√5 - 7√7), we can combine like terms.

The terms 12√5 and 6√5 have the same radical (√5), so we can add their coefficients, which gives us 18√5.

The terms -7√7 and -7√7 also have the same radical (√7), so we can add their coefficients, which gives us -14√7.

Combining these simplified terms, we have 18√5 - 14√7 as the simplified expression.

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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.