How do you simplify #5sqrt3(6sqrt10-6sqrt3)#?

Answer 1

#30(sqrt30-3)#

We essentially have the following

#color(blue)(5)color(lime)(sqrt3)*color(blue)(6)color(lime)(sqrt10)-color(blue)(5)color(lime)(sqrt3)*color(blue)(6)color(lime)(sqrt3)#

Which can be simplified if we multiply the integers and square roots together, respectively. We'll get

#color(blue)((5*6))color(lime)(sqrt3sqrt10)-color(blue)((5*6))color(lime)(sqrt3sqrt3)#

Which simplifies to

#color(blue)(30)color(lime)(sqrt30)-color(blue)(30)*color(lime)(3)#
#=>color(blue)(30)color(lime)(sqrt30)-90#
Since #30# has no perfect square factors, we cannot simplify the radical any further. We can factor a #30# out of both terms, however. We get
#30(sqrt30-3)#

Hope this helps!

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Answer 2

To simplify the expression 5√3(6√10 - 6√3), we can use the distributive property.

First, distribute 5√3 to both terms inside the parentheses:

5√3 * 6√10 = 30√30

5√3 * -6√3 = -30√9

Simplifying further:

30√30 - 30√9

√30 is not simplified, but √9 simplifies to 3:

30√30 - 30 * 3

30√30 - 90

Therefore, the simplified expression is 30√30 - 90.

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Answer 3

To simplify (5\sqrt{3}(6\sqrt{10} - 6\sqrt{3})), you can distribute (5\sqrt{3}) to both terms inside the parentheses:

[5\sqrt{3}(6\sqrt{10} - 6\sqrt{3}) = 30\sqrt{30} - 30\sqrt{9}]

Since (\sqrt{9} = 3), the expression further simplifies to:

[30\sqrt{30} - 30(3)]

Finally, multiplying (30) by (3), we get:

[30\sqrt{30} - 90]

So, (5\sqrt{3}(6\sqrt{10} - 6\sqrt{3})) simplifies to (30\sqrt{30} - 90).

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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.

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.

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.

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.

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