Certainly, let's solve the problem step-by-step.
We have the expression [tex]\(\frac{\sqrt{35}}{\sqrt{7}}\)[/tex], and we want to simplify it using the property [tex]\(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\)[/tex].
### Step 1: Identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex]
Here, [tex]\(a = 35\)[/tex] and [tex]\(b = 7\)[/tex].
### Step 2: Apply the Property
According to the property [tex]\(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\)[/tex], we can rewrite the expression:
[tex]\[\frac{\sqrt{35}}{\sqrt{7}} = \sqrt{\frac{35}{7}}\][/tex]
### Step 3: Simplify the Fraction Inside the Square Root
Next, we need to simplify the fraction inside the square root:
[tex]\[\frac{35}{7} = 5\][/tex]
### Step 4: Substitute Back into the Expression
Now, substituting back, we get:
[tex]\[\sqrt{\frac{35}{7}} = \sqrt{5}\][/tex]
Hence, the simplified form of [tex]\(\frac{\sqrt{35}}{\sqrt{7}}\)[/tex] is [tex]\(\sqrt{5}\)[/tex].
### Final Answer
Thus, the choice equivalent to the quotient [tex]\(\frac{\sqrt{35}}{\sqrt{7}}\)[/tex] is:
E. [tex]\(\sqrt{5}\)[/tex]
