The Choice is equivalent to the quotient shown here when x >= 0 is C; [tex]\dfrac{3\sqrt{ x} }{5}[/tex].
What are equivalent expressions?
Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
Given;
[tex]\dfrac{\sqrt{18x} }{\sqrt{50} }[/tex]
To find equivalent to the quotient,
[tex]\dfrac{\sqrt{18x} }{\sqrt{50} }[/tex]
Both the numerator and denominator have same square root so we have to take square root in common.
Apply exponential property, a^m divide [tex]a^m= a^{m-n}[/tex]
Now, Subtract the exponents when the base of exponents are same and the exponents are in division.
[tex]\dfrac{\sqrt{3\times 3 \times 2x} }{\sqrt{5 \times 2 \times5} }\\\\\\\dfrac{3\sqrt{ 2x} }{5\sqrt{2} }\\\\\\\dfrac{3\sqrt{ x} }{5}[/tex]
Thus, the Choice is equivalent to the quotient shown here when x >= 0 is C; [tex]\dfrac{3\sqrt{ x} }{5}[/tex].
Learn more about equivalent expressions;
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