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According to the property [tex]$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$[/tex], which choice is equivalent to the quotient below?

[tex]\[
\frac{\sqrt{35}}{\sqrt{7}}
\][/tex]

A. [tex]$-\sqrt{5}$[/tex]

B. 25

C. 5

D. -5

E. [tex]$\sqrt{5}$[/tex]

Sagot :

GinnyAnsweridn
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]
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