simplify the folloing by rationalising the denominator
(3+square root 2)
-------------------------
(4-square root 2)
please can you explain how you do it. cheers
2007-09-15 23:10:59 · 3 answers · asked by londonlad90 1 in Science & Mathematics ➔ Mathematics
(3 + sqrt(2)) / (4 - sqrt(2))
= [(3 + sqrt(2)) / (4 - sqrt(2))] * [(4 + sqrt(2)) / (4 + sqrt(2))]
= [(3 + sqrt(2))(4 + sqrt(2))] / [(4 - sqrt(2))(4 + sqrt(2))]
= [12 + 3sqrt(2) + 4sqrt(2) + 2] / [4² - (sqrt(2))²]
= [14 + 7sqrt(2)] / 14
= 1 + 0.5 sqrt(2)
2007-09-15 23:26:55 · answer #1 · answered by gudspeling 7 · 1⤊ 0⤋
= (3 + â2)(4 + â2) / (16 - 2)
= (12 + 7â2 + 2) / 14
= (14 + 7â2) / 14
= 1 + (1/2) â2
2007-09-16 06:51:15 · answer #2 · answered by Como 7 · 2⤊ 0⤋
there should be no radicals (ie squareroots) in the denominator...
given
(3+â2) / (4 - â2)
to rationalize we need to multiply it with the conjugate of the denominator, eg. the binomial with an opposite sign..
this means that we need to multiply with (4+â2) / (4+â2)
thus...
(3+â2) / (4 - â2) * (4+â2) / (4+â2)
= (12 + 4â2 + 3â2 + 2) / (16 - 2)
= (14 + 7â2) / 14
= 1 + â2/2
2007-09-16 06:35:36 · answer #3 · answered by quigonjan 3 · 0⤊ 2⤋