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# Simplify the product of radicals $2\sqrt{3-5}\sqrt{7}\cdot 2\sqrt{3+5\sqrt{7}}$

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##  Final answer to the problem

$4\sqrt{42+70\sqrt{7}}i$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Write in simplest form
• Prime Factor Decomposition
• Solve by quadratic formula (general formula)
• Find the derivative using the definition
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
Can't find a method? Tell us so we can add it.
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Subtract the values $3$ and $-5$

$2\sqrt{-2}\sqrt{7}\cdot 2\sqrt{3+5\sqrt{7}}$

Learn how to solve product of radicals problems step by step online.

$2\sqrt{-2}\sqrt{7}\cdot 2\sqrt{3+5\sqrt{7}}$

Learn how to solve product of radicals problems step by step online. Simplify the product of radicals 2(3-5)^(1/2)7^(1/2)*2(3+57^(1/2))^(1/2). Subtract the values 3 and -5. Multiply 2 times 2. Calculate the power \sqrt{-2} using complex numbers. Apply the property of power of a product in reverse: a^n\cdot b^n=(a\cdot b)^n.

##  Final answer to the problem

$4\sqrt{42+70\sqrt{7}}i$

##  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

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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

###  Main Topic: Product of Radicals

The product of radicals is an expression that involves the multiplication of two or more radicals.