ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

Simplify the expression $9^{\frac{1}{3}}\left(\sqrt{2}+1\right)^{\frac{1}{3}}\left(27-2\sqrt{162}\right)^{\frac{1}{6}}$

Go!
Symbolic mode
Text mode
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
|◻|
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

 Final answer to the problem

$3\sqrt[3]{\sqrt{2}+1}\sqrt[6]{3-2\sqrt{2}}$
Got another answer? Verify it here!

 Step-by-step Solution 

How should I solve this problem?

• Simplify
• Prime Factor Decomposition
• Solve by quadratic formula (general formula)
• Find the derivative using the definition
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
• Find break even points
Can't find a method? Tell us so we can add it.
1

Divide $1$ by $3$

$\sqrt[3]{9}\left(\sqrt{2}+1\right)^{\frac{1}{3}}\left(27-2\sqrt{162}\right)^{\frac{1}{6}}$

Learn how to solve problems step by step online.

$\sqrt[3]{9}\left(\sqrt{2}+1\right)^{\frac{1}{3}}\left(27-2\sqrt{162}\right)^{\frac{1}{6}}$

Learn how to solve problems step by step online. Simplify the expression 9^(1/3)(2^1/2+1)^(1/3)(27-2162^1/2)^(1/6). Divide 1 by 3. Divide 1 by 3. Divide 1 by 6. Calculate the cubic root of 9.

 Final answer to the problem

$3\sqrt[3]{\sqrt{2}+1}\sqrt[6]{3-2\sqrt{2}}$

 Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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
|◻|
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