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Simplify the product of radicals $\sqrt{\sqrt{10}+\sqrt{5}}\sqrt{\sqrt{10}-\sqrt{5}}$

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 Final answer to the problem

$\sqrt{5}$
Got another answer? Verify it here!

 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.
1

Apply the property of power of a product in reverse: $a^n\cdot b^n=(a\cdot b)^n$

$\sqrt{\left(\sqrt{10}+\sqrt{5}\right)\cdot \left(\sqrt{10}-\sqrt{5}\right)}$
2

Solve the product of difference of squares $\left(\sqrt{10}+\sqrt{5}\right)\cdot \left(\sqrt{10}-\sqrt{5}\right)$

$\sqrt{5}$

 Final answer to the problem

$\sqrt{5}$

$2.236068$

 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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1
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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

 Main Topic: Product of Radicals

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