Respuesta :
Answer:
what is √25x^2y^2/√xy in simplest from? Assume x≥o and y≥0
The correct answer to this question is 5√xy
Step-by-step explanation:
The given expression in its simplest form is [tex]5 \sqrt{xy}[/tex]
From the question,
We are to evaluate sqrt 25x^2y^2/sqrt xy in its simplest form.
First, we will write the given expression properly
The given expression is
[tex]\frac{\sqrt{25x^{2} y^{2} } }{\sqrt{xy} }[/tex]
Now, the expression can be evaluated as shown below
[tex]\frac{\sqrt{25x^{2} y^{2} } }{\sqrt{xy} }[/tex]
[tex]\frac{\sqrt{25 } \times \sqrt{x^{2} y^{2}} }{\sqrt{xy} }[/tex]
This becomes
[tex]\frac{5 \times xy }{\sqrt{xy} }[/tex]
This becomes
[tex]\frac{5 \times xy}{(xy)^{\frac{1}{2} } }[/tex]
This can be written as
[tex]5 \times xy \div (xy)^{\frac{1}{2} }[/tex]
By applying one of the laws of indices
We get,
[tex]5 \times (xy)^{1-\frac{1}{2} }[/tex]
[tex]5 \times (xy)^{\frac{1}{2} }[/tex]
[tex]5 \times \sqrt{xy}[/tex]
[tex]5 \sqrt{xy}[/tex]
Hence, the given expression in its simplest form is [tex]5 \sqrt{xy}[/tex]
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