Home > Algebra > Multiplication and Division of Radicals

How do you simplify #sqrt96divsqrt8#?

Answer 1

Eva Adamson

# =color(red)( (2sqrt6)/sqrt2#

#sqrt96/sqrt8#

#sqrt 96 = 4sqrt6# # sqrt8 = 2sqrt2#

rewriting the expression: #(4sqrt6) / (2sqrt2)# # =color(red)( (2sqrt6)/sqrt2#

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

Answer 2

Jace Anderson

To simplify sqrt96 divided by sqrt8, we can simplify the square roots separately and then divide the simplified values.

First, let's simplify sqrt96. We can break down 96 into its prime factors: 2 * 2 * 2 * 2 * 3. Taking out pairs of the same prime factors, we have 2 * 2 * 2 * sqrt3. Simplifying further, we get 8 * sqrt3.

Next, let's simplify sqrt8. We can break down 8 into its prime factors: 2 * 2 * 2. Taking out pairs of the same prime factors, we have 2 * sqrt2.

Now, we can divide the simplified values: (8 * sqrt3) / (2 * sqrt2). Dividing the numbers, we get 4 * sqrt3 / sqrt2.

To simplify further, we rationalize the denominator by multiplying both the numerator and denominator by sqrt2: (4 * sqrt3 * sqrt2) / (sqrt2 * sqrt2). Simplifying, we have (4 * sqrt6) / 2.

Finally, we can simplify the expression to 2 * sqrt6.

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.