Question

What is the following quotient? √96/√8

Answer 1

Answer:

$2\sqrt{3}$

Step-by-step explanation:

We are asked to find the quotient of expression: $\frac{\sqrt{96}}{\sqrt{8}}$

Upon using the quotient rules for radicals we will get,  

$\frac{\sqrt{96}}{\sqrt{8}} =\sqrt{\frac{96}{8}$

Now let us cancel out GCF of 96 and 8.

$\sqrt{\frac{96}{8}}=\sqrt{12}$

Now let us factor out perfect square from $\sqrt{12}$

$\sqrt{12}=\sqrt{4}\times\sqrt{3}$

$\sqrt{4}\times\sqrt{3}=2\sqrt{3}$

Therefore, our radical expression simplifies to $2\sqrt{3}$.

Answer 2

By using the fact that the square root is distributive under division, we will see that:

$\sqrt{96} \sqrt{8} = \sqrt{96/8} = \sqrt{12} = 3.464$

How to solve a quotient of square roots?

Here you need to know that the square root is distributive under multiplication/division.

This means that:

$\sqrt{x} /\sqrt{y} = \sqrt{x/y}$

Now, if we apply that to the given quotient, we will get:

$\sqrt{96} \sqrt{8} = \sqrt{96/8} = \sqrt{12}$

Now we can also give the exact solution, as we know that:

√12 = 3.464

If you want to learn more about radical equations, you can read:

https://brainly.com/question/8952483