How do you simplify 3−4√34√5+3√2?

1 Answer
Shwetank Mauria
Jan 24, 2017

3−4√34√5+3√2=12√5−9√2−16√15+12√662

Explanation:

To simplify 3−4√34√5+3√2, what we need to do is to multiply numerator and denominator by the conjugate of its irrational denominator.

Conjugate of a irrational number (√a±√b) is (√a∓√b). (If we just have √p in denominator, then just multiplying numerator and denominator by √p suffices.)

Hence, 3−4√34√5+3√2

= (3−4√3)(4√5−3√2)(4√5+3√2)(4√5−3√2)

= 3(4√5−3√2)−4√3(4√5−3√2)(4√5)2−(3√2)2

= 12√5−9√2−16√15+12√680−18

= 12√5−9√2−16√15+12√662

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