Simplify (4 square root of 2)/(8 square root of 10)

Math
42810
Cancel the common factor of 4 and 8.
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Factor 4 out of 42.
4(2)810
Cancel the common factors.
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Factor 4 out of 810.
4(2)4(210)
Cancel the common factor.
424(210)
Rewrite the expression.
2210
2210
2210
Combine 2 and 10 into a single radical.
2102
Cancel the common factor of 2 and 10.
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Factor 2 out of 2.
2(1)102
Cancel the common factors.
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Factor 2 out of 10.
2⋅12⋅52
Cancel the common factor.
2⋅12⋅52
Rewrite the expression.
152
152
152
Simplify the numerator.
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Rewrite 15 as 15.
152
Any root of 1 is 1.
152
Multiply 15 by 55.
15⋅552
Combine and simplify the denominator.
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Multiply 15 and 55.
5552
Raise 5 to the power of 1.
55152
Raise 5 to the power of 1.
551512
Use the power rule aman=am+n to combine exponents.
551+12
Add 1 and 1.
5522
Rewrite 52 as 5.
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Use axn=axn to rewrite 5 as 512.
5(512)22
Apply the power rule and multiply exponents, (am)n=amn.
5512⋅22
Combine 12 and 2.
55222
Cancel the common factor of 2.
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Cancel the common factor.
55222
Divide 1 by 1.
5512
5512
Evaluate the exponent.
552
552
552
552
Multiply the numerator by the reciprocal of the denominator.
55⋅12
Multiply 55⋅12.
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Multiply 55 and 12.
55⋅2
Multiply 5 by 2.
510
510
The result can be shown in multiple forms.
Exact Form:
510
Decimal Form:
0.22360679…
Simplify (4 square root of 2)/(8 square root of 10)

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