To calculate: The simplification of the expression \frac{y-3}{\sqrt{y}+\sqrt{3}}

Tammy Todd 2021-08-14 Answered
To calculate: The simplification of the expression \(\displaystyle{\frac{{{y}-{3}}}{{\sqrt{{{y}}}+\sqrt{{{3}}}}}}\)
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Expert Answer

Demi-Leigh Barrera
Answered 2021-08-15 Author has 25105 answers
Calculation:
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Answered 2021-12-24 Author has 0 answers

Step 1

Consider the expressions as,

\(\frac{y-3}{\sqrt y+\sqrt3}\)

To simplify the expression, rationalise the denomination and simplify the radical in the denomination

So,

\(\frac{y-3}{\sqrt y+\sqrt3}=\frac{y-3}{\sqrt y+\sqrt 3} \times \frac{\sqrt y-\sqrt 3}{\sqrt y-\sqrt 3}\)

\(=\frac{(y-3)(\sqrt y-\sqrt3)}{(\sqrt y)^2-(\sqrt 3)^2}\)

\(=\frac{(y-3)(\sqrt y-\sqrt 3)}{(y-3)}\)

\(=\sqrt y-\sqrt3\)

Hence, the simplification of the given expression is \(\sqrt y-\sqrt3\)

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