The value of the expression [tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex] after rationalizing the denominator is [tex]\frac{2\sqrt{5}+5 }{5}[/tex].
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a square root or a cube root, from the fraction's denominator to its numerator (numerator).
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex]
Now, let [tex]y=\frac{2+\sqrt{5} }{\sqrt{5} }[/tex]
To rationalize the denominator we multiply and divide the expression by √5.
[tex]y=\frac{2+\sqrt{5} }{\sqrt{5} } \times \frac{\sqrt{5} }{\sqrt{5} }[/tex]
[tex]y=\frac{2\sqrt{5}+(\sqrt{5} )^{2} }{(\sqrt{5} )^{2}}[/tex]
[tex]y=\frac{2\sqrt{5}+5 }{5}[/tex]
The value of the expression when rationalized [tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex] is [tex]\frac{2\sqrt{5}+5 }{5}[/tex].
Learn more about rationalizing here:
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