Solve the equation $s=\left(\sqrt[8]{2}+1\right)\left(\sqrt[8]{2}-1\right)\left(\sqrt[4]{2}+1\right)\left(\sqrt{2}+1\right)\sqrt{2}$

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Final answer to the problem

$s=\left(\sqrt[4]{2}+1\right)\left(\sqrt{2}+1\right)\left(\sqrt[4]{2}-1\right)\sqrt{2}$
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Step-by-step Solution

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1

The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: $(a+b)(a-b)=a^2-b^2$.

$s=\left(\left(\sqrt[8]{2}\right)^2-1\right)\left(\sqrt[4]{2}+1\right)\left(\sqrt{2}+1\right)\sqrt{2}$

Learn how to solve one-variable linear equations problems step by step online.

$s=\left(\left(\sqrt[8]{2}\right)^2-1\right)\left(\sqrt[4]{2}+1\right)\left(\sqrt{2}+1\right)\sqrt{2}$

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Learn how to solve one-variable linear equations problems step by step online. Solve the equation s=(2^(1/8)+1)(2^(1/8)-1)(2^(1/4)+1)(2^(1/2)+1)2^(1/2). The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Simplify \left(\sqrt[8]{2}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{8} and n equals 2. Multiply the fraction and term in 2\left(\frac{1}{8}\right). Divide 2 by 8.

Final answer to the problem

$s=\left(\sqrt[4]{2}+1\right)\left(\sqrt{2}+1\right)\left(\sqrt[4]{2}-1\right)\sqrt{2}$

Exact Numeric Answer

$s=1.4142135$

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Function Plot

Plotting: $s-\left(\sqrt[8]{2}+1\right)\left(\sqrt[8]{2}-1\right)\left(\sqrt[4]{2}+1\right)\left(\sqrt{2}+1\right)\sqrt{2}$

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7
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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

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Main Topic: One-variable linear equations

Algebraic equations that have just one variable.

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