Answered

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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{30}}{\sqrt{5}} [/tex]

A. [tex] -\sqrt{6} [/tex]

B. [tex] \sqrt{6} [/tex]

C. 6

D. 36

E. -6

Sagot :

GinnyAnswer
Let's solve the given question step-by-step.

We are given the expression:
[tex]\[ \frac{\sqrt{30}}{\sqrt{5}} \][/tex]

According to the property of square roots, we can rewrite the given expression as:
[tex]\[ \frac{\sqrt{30}}{\sqrt{5}} = \sqrt{\frac{30}{5}} \][/tex]

Now, we need to simplify the fraction inside the square root:
[tex]\[ \frac{30}{5} \][/tex]

Perform the division:
[tex]\[ \frac{30}{5} = 6 \][/tex]

So, now the expression becomes:
[tex]\[ \sqrt{6} \][/tex]

Therefore, the equivalent expression is:
[tex]\[ \sqrt{6} \][/tex]

Thus, the correct choice is:
[tex]\[ \boxed{\sqrt{6}} \][/tex]
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