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Rationalise the denominator5+54√3 |
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Answer» Step-by-step explanation: We rationalise the DENOMINATOR of ( 3 2
− 5
5 2
− 3
) by MULTIPLYING its rationalising FACTOR (3 2
+ 5
) in the numerator and denominator as follows:
3 2
− 5
5 2
− 3
× 3 2
+ 5
3 2
+ 5
= (3 2
− 5
)(3 2
+ 5
) (5 2
− 3
)(3 2
+ 5
)
= (3 2
) 2 −( 5
) 2
5 2
(3 2
+ 5
)− 3
(3 2
+ 5
)
= (9×2)−5 (5×3 2×2
)+(5 2×5
)−(3 3×2
)−( 3×5
)
= 18−5 15 4
+5 10
−3
− 15
= (15×2)+5 10
−3 6
− 15
= 13 30+5 10
−3 6
− 15
Hence, 3 2
− 5
5 2
− 3
= 13 30+5 10
−3 6
− 15
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