# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{\sqrt{x+5}-\sqrt{5}}{x}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\sqrt{x+5}-\sqrt{5}}{x}\frac{\sqrt{x+5}+\sqrt{5}}{\sqrt{x+5}+\sqrt{5}}\right)$

Learn how to solve limits problems step by step online. Evaluate the limit of ((x+5)^0.5-5^0.5)/x as x approaches 0. Applying rationalisation. Multiplying fractions. Solve the product of difference of squares \left(\sqrt{x+5}-\sqrt{5}\right)\left(\sqrt{x+5}+\sqrt{5}\right). Simplifying.

$\frac{36}{161}$$\,\,\left(\approx 0.22360679774997896\right)$

### Problem Analysis

$\lim_{x\to0}\left(\frac{\sqrt{x+5}-\sqrt{5}}{x}\right)$

Limits

~ 0.4 seconds