Answer:
a) 2
b) [tex]\frac{4x}{y}[/tex]
Step-by-step explanation:
a) [tex]\frac{\sqrt{500} }{\sqrt{5} }[/tex]
We can rewrite 500 as 100*5 and 100 is [tex]10^2[/tex] causing the 10 to come out of the root.
[tex]\frac{10\sqrt{5} }{\sqrt{5} }[/tex]
Rationalize.
[tex]\frac{10\sqrt{5} }{\sqrt{5} }*\frac{\sqrt{5} }{\sqrt{5} } =\frac{10}{5}=2[/tex]
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b) [tex]\frac{\sqrt{48x^3} }{\sqrt{3xy^2} }[/tex]
48 can be rewritten as 6*8 and 8 can be rewritten as [tex]2^2*2[/tex]
[tex]\frac{\sqrt{6*2^2*2x^3} }{\sqrt{3xy^2} }[/tex]
[tex]\frac{2\sqrt{6*2x^3} }{\sqrt{3xy^2} }[/tex]
[tex]\frac{2\sqrt{12x^3} }{\sqrt{3xy^2} }[/tex]
12 can be rewritten as 4*3 and 4 can be rewritten as [tex]2^2[/tex]
[tex]\frac{2\sqrt{2^2*3x^3} }{\sqrt{3xy^2} }[/tex]
[tex]\frac{2*2\sqrt{3x^3} }{\sqrt{3xy^2} }[/tex]
[tex]\frac{4\sqrt{3x^3} }{\sqrt{3xy^2} }[/tex]
[tex]x^3[/tex] is the same as [tex]x^2*x[/tex] causing x to come out of the root, as well as y.
[tex]\frac{4x\sqrt{3x} }{y\sqrt{3x} }[/tex]
Rationalize
[tex]\frac{4x\sqrt{3x} }{y\sqrt{3x} }*\frac{\sqrt{3x} }{\sqrt{3x} } =\frac{4x*3x}{y*3x} =\frac{12x^2}{3xy}=\frac{4x}{y}[/tex]
