How do you simplify #sqrt(54y^2)/ sqrt(6y)#?

Answer 1

Eva Abramson

#3.sqrt y#

#sqrt(54y^2)/sqrt(6y)#

#(sqrt(6).sqrt(9).sqrt(y^2))/(sqrt(6) sqrt(y))#

#(cancel(sqrt(6)).sqrt(9).sqrt(y^2))/(cancelsqrt(6) sqrt(y))#

#(.sqrt(9).sqrt(y^2))/( sqrt(y))#

#(3.y)/( sqrt(y))#

#3.sqrt y#

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Answer 2

Jace Anderson

To simplify the expression sqrt(54y^2)/sqrt(6y), we can combine the square roots by dividing the numbers inside the square roots.

First, let's simplify the numbers inside the square roots: sqrt(54y^2) = sqrt(9 * 6 * y^2) = sqrt(9) * sqrt(6) * sqrt(y^2) = 3 * sqrt(6) * y

Next, let's simplify the denominator: sqrt(6y) = sqrt(6) * sqrt(y)

Now, we can divide the numerator by the denominator: (3 * sqrt(6) * y) / (sqrt(6) * sqrt(y))

Since the square root of 6 appears in both the numerator and denominator, we can cancel them out: (3 * y) / sqrt(y)

Therefore, the simplified expression is (3y) / sqrt(y).

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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.