What is the limit as p approaches 9 of (sqrt(p)-3)/(sqrt(1+\sqrt{p))-2} ?

The limit as p approaches 9 of (sqrt(p)-3)/(sqrt(1+\sqrt{p))-2} is 4

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limit as p approaches 9 of (sqrt(p)-3)/(sqrt(1+\sqrt{p))-2}

p \to 9 lim (\frac{p - 3}{1 + p - 2})

4

Solution steps

p \to 9 lim (\frac{p - 3}{1 + p - 2})

Rationalize denominator

\frac{p - 3}{1 + p - 2} : p + 1 + 2

= p \to 9 lim (p + 1 + 2)

Plug in the value

p = 9

= 9 + 1 + 2

Simplify

9 + 1 + 2 : 4

= 4

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What is the limit as p approaches 9 of (sqrt(p)-3)/(sqrt(1+\sqrt{p))-2} ?
The limit as p approaches 9 of (sqrt(p)-3)/(sqrt(1+\sqrt{p))-2} is 4