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How do you simplify #4sqrt5(3sqrt5+8sqrt2)#?

Answer 1

Eva Adamson

#92sqrt2sqrt5#

#4sqrt5(3sqrt5+8sqrt2)#

#:.=4sqrt5 xx 3sqrt5+4sqrt5 xx 8sqrt2#

#:.=sqrt5 xx sqrt5=5#

#:.=(12 xx 5)+32 xx sqrt5 xx sqrt2#

#:.=60+32 xx sqrt5 xx sqrt2#

#:.=92sqrt2sqrt5#

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Answer 2

Jace Anderson

To simplify the expression 4√5(3√5+8√2), you can use the distributive property. Multiply 4√5 by each term inside the parentheses:

4√5 * 3√5 = 12√(55) = 12√25 = 125 = 60

4√5 * 8√2 = 32√(5*2) = 32√10

Therefore, the simplified expression is 60 + 32√10.

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Answer 3

Nathan Axel

To simplify ( 4\sqrt{5}(3\sqrt{5} + 8\sqrt{2}) ), you can use the distributive property:

[ 4\sqrt{5}(3\sqrt{5} + 8\sqrt{2}) = 4\sqrt{5} \times 3\sqrt{5} + 4\sqrt{5} \times 8\sqrt{2} ]

Now, simplify each term:

[ 4\sqrt{5} \times 3\sqrt{5} = 12 \times \sqrt{5} \times \sqrt{5} = 12 \times 5 = 60 ]

[ 4\sqrt{5} \times 8\sqrt{2} = 32 \times \sqrt{5} \times \sqrt{2} = 32\sqrt{10} ]

So, the simplified expression is ( 60 + 32\sqrt{10} ).

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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.