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How do you simplify #(20sqrt18) / (5sqrt3)#?

Answer 1

Julia Adams

#4sqrt(6)#

#(20sqrt(18))/(5(sqrt(3)))#

#=20/5 xx sqrt(18)/sqrt(3)#

#= 4 xx (cancel(sqrt(3))xxsqrt(6))/cancel(sqrt(3))#

#= 4 sqrt(6)#

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Answer 2

Savannah Anderson

To simplify the expression (20sqrt18) / (5sqrt3), we can simplify the square roots separately and then divide the resulting numbers.

First, simplify the square root of 18: √18 = √(9 * 2) = √9 * √2 = 3√2

Next, simplify the square root of 3: √3 = √(3 * 1) = √3 * √1 = √3

Now, substitute these simplified square roots back into the expression: (20sqrt18) / (5sqrt3) = (20 * 3√2) / (5 * √3)

Simplify the numbers outside the square roots: 20/5 = 4

Combine the square roots: (4 * 3√2) / √3 = 12√2 / √3

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator: (12√2 / √3) * (√3 / √3) = (12√2 * √3) / (√3 * √3) = (12√6) / 3

Simplify the expression further: (12√6) / 3 = 4√6

Therefore, the simplified form of (20sqrt18) / (5sqrt3) is 4√6.

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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.