Simplify ( square root of 6- square root of 5i)( square root of 6+ square root of 5i)

Math
(6-5i)(6+5i)
Expand (6-5i)(6+5i) using the FOIL Method.
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Apply the distributive property.
6(6+5i)-5i(6+5i)
Apply the distributive property.
66+65i-5i(6+5i)
Apply the distributive property.
66+65i-5i6-5i5i
66+65i-5i6-5i5i
Simplify and combine like terms.
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Simplify each term.
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Combine using the product rule for radicals.
6⋅6+65i-5i6-5i5i
Multiply 6 by 6.
36+65i-5i6-5i5i
Rewrite 36 as 62.
62+65i-5i6-5i5i
Pull terms out from under the radical, assuming positive real numbers.
6+65i-5i6-5i5i
Combine using the product rule for radicals.
6+6(5i)-5i6-5i5i
Multiply 6 by 5.
6+30i-5i6-5i5i
Multiply -5i6.
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Combine using the product rule for radicals.
6+30i-6(5i)-5i5i
Multiply 6 by 5.
6+30i-30i-5i5i
6+30i-30i-5i5i
Multiply -5i5i.
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Raise 5i to the power of 1.
6+30i-30i-(5i15i)
Raise 5i to the power of 1.
6+30i-30i-(5i15i1)
Use the power rule aman=am+n to combine exponents.
6+30i-30i-5i1+1
Add 1 and 1.
6+30i-30i-5i2
6+30i-30i-5i2
Rewrite 5i2 as 5i.
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Use axn=axn to rewrite 5i as (5i)12.
6+30i-30i-((5i)12)2
Apply the power rule and multiply exponents, (am)n=amn.
6+30i-30i-(5i)12⋅2
Combine 12 and 2.
6+30i-30i-(5i)22
Cancel the common factor of 2.
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Cancel the common factor.
6+30i-30i-(5i)22
Divide 1 by 1.
6+30i-30i-(5i)1
6+30i-30i-(5i)1
Simplify.
6+30i-30i-(5i)
6+30i-30i-(5i)
Multiply 5 by -1.
6+30i-30i-5i
6+30i-30i-5i
Subtract 30i from 30i.
6+0-5i
Add 6 and 0.
6-5i
6-5i
Simplify ( square root of 6- square root of 5i)( square root of 6+ square root of 5i)

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