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Surds maths question to settle a bet, please help?
Me and my friend had a mock test paper today and there was a question on surds, we both had alternate methods and answers, please help us find the answer to
(root75 - 2root3)^2
Please show working
6 Answers
- 9 years agoFavorite Answer
(√75 - 2√3)²
= (5√3 - 2√3)²
= (3√3)²
= (√27)²
= 27
Whatever may be method the answer is 27 without any doubt.
- ?Lv 79 years ago
I have no idea what a surd is but:
(â75 - 2â3)^2
= 75 -(2â3â75) - (2â3â75) + 4(3)
= 75 - 2(2â3â75) + 12
= 87 - 4â3â75
= 87 - 4â3â(25*3)
= 87 - 4â3 5â3
= 87 - 20â3â3
= 87 - 20(3)
= 87 - 60
= 27
- Elizabeth MLv 79 years ago
=(root75)^2 -4root75root3+4(root3)^2
=75 - 4root(225)+12
=75-60+12
=27
Its a good idea to use a=root75 and b=root3 and then square
(a-2b) giving a^2-4ab+4b^2 and you can square the bits.
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- BrianLv 79 years ago
(sqrt(75) - 2*sqrt(3))^2 = 75 - 4*sqrt(3*75) + 4*3 = 87 - 4*sqrt(225) = 87 - 4*15 = 27.
- 9 years ago
sq rt 75 - 2 root 3
sq rt 75 - 2 root 3
----------------------------
-2 sq rt 225- 4 root 9
-2sq rt 225
75
---------------------------------
75-60- 12= 3
