Simplify ( square root of 6)/( square root of 5+ square root of 2)

Math
65+2
Multiply 65+2 by 5-25-2.
65+2⋅5-25-2
Multiply 65+2 and 5-25-2.
6(5-2)(5+2)(5-2)
Expand the denominator using the FOIL method.
6(5-2)52-10+10-22
Simplify.
6(5-2)3
Apply the distributive property.
65+6(-2)3
Combine using the product rule for radicals.
6⋅5+6(-2)3
Multiply 6(-2).
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Combine using the product rule for radicals.
6⋅5-6⋅23
Multiply 6 by 2.
6⋅5-123
6⋅5-123
Simplify each term.
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Multiply 6 by 5.
30-123
Rewrite 12 as 22⋅3.
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Factor 4 out of 12.
30-4(3)3
Rewrite 4 as 22.
30-22⋅33
30-22⋅33
Pull terms out from under the radical.
30-(23)3
Multiply 2 by -1.
30-233
30-233
The result can be shown in multiple forms.
Exact Form:
30-233
Decimal Form:
0.67104131…
Simplify ( square root of 6)/( square root of 5+ square root of 2)

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