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# Find the limit of $\frac{\sqrt{x+6}-4}{x-10}$ as $x$ approaches $10$

## Step-by-step Solution

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$\frac{1}{8}$
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## Step-by-step Solution

Problem to solve:

$\lim_{x\to\:10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$

Specify the solving method

1

Applying rationalisation

$\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}\right)$

Learn how to solve limits problems step by step online. Find the limit of ((x+6)^1/2-4)/(x-10) as x approaches 10. Applying rationalisation. Multiplying fractions \frac{\sqrt{x+6}-4}{x-10} \times \frac{\sqrt{x+6}+4}{\sqrt{x+6}+4}. Solve the product of difference of squares \left(\sqrt{x+6}-4\right)\left(\sqrt{x+6}+4\right). Expand and simplify -10+x.

$\frac{1}{8}$

$0.125$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
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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
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\lim_{x\to\:10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$