Home > Algebra > Multiplication and Division of Radicals

How do you simplify #(12sqrt9)/sqrt18#?

Answer 1

Nathan Axel

# = 6sqrt2 #

#(12sqrt9)/ sqrt18#

#sqrt 9 = sqrt ( 3 *3 ) = color(green)(3 #

#sqrt18 = sqrt ( 2 * 3 * 3 ) = sqrt ( 2 * 3 ^2) = color(green)( 3 sqrt2 #

Our expression now becomes #(12 * color(green)((3)))/ color(green)( 3 sqrt2 #

# = (12 * color(green)(cancel(3)))/ color(green)( cancel3 * sqrt2 #

# = 12 / sqrt2 #

Rationalising the denominator: # = (12 * sqrt2) / (sqrt2 * sqrt2) #

# = (12 * sqrt2) / 2 #

# = (cancel12 * sqrt2) / cancel 2 #

# = 6sqrt2 #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Savannah Anderson

To simplify (12√9)/√18, we can simplify the square roots and then divide.

First, we simplify the square roots: √9 = 3 √18 = √(9 * 2) = √9 * √2 = 3√2

Now, we substitute the simplified square roots back into the expression: (12 * 3)/(3√2)

Next, we cancel out the common factor of 3: (12 * 1)/(√2)

Finally, we simplify the expression: 12/√2 = (12/√2) * (√2/√2) = (12√2)/2 = 6√2

Therefore, (12√9)/√18 simplifies to 6√2.

By signing up, you agree to our Terms of Service and Privacy Policy

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.