Question

What is the following quotient? Sqrt 96/ Sqrt 8

Answer 1

Answer:

The quotient of given expression is 2√3.

Step-by-step explanation:

The given expression is

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

According to the properties of radical expressions.

$\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$

Using this property, we get

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

Cancel out the common factors.

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

$\frac{\sqrt{96}}{\sqrt{8}}=\sqrt{4\times 3}$

$\frac{\sqrt{96}}{\sqrt{8}}=\sqrt{2^2\times 3}$

$\frac{\sqrt{96}}{\sqrt{8}}=2\sqrt{3}$

Therefore the quotient of given expression is 2√3.

Answer 2

Radicals cannot exist as a denominator, so you would multiply both Sqrt96 and Sqrt8 by the Sqrt8, giving you Sqrt768 over 8 (since a sqrt times itself is the base number, in this case 8) then you would simplify Sqrt768 into 16 x Sqrt3, leaving you with 16xSqrt3 over 8. simplify into 2Sqrt3 by dividing.