Question

Solve 4-root5 /3 - root2

Answer 1

To simplify :- 4 - √5/3 - √2

Used Concept :- Rationalization

Used Formulae :- a²-b² = (a+b) (a-b)

Important Points to remember in these questions :-

( i ) We can also rationalize numerator .

( ii ) We wan to get correct answer . But we didn't know that we have to rationalize at numerator or denominator . So we have to rationalize at that whose either denominator or numerator is single.

Solution :-

$\frac{4 - \sqrt{5} }{3 - \sqrt{2} }$

On Rationalising the denominator we get,

$\frac{4 - \sqrt{5} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} }$

Now we will use the above identity.

$\frac{(4 - \sqrt{5})(3 + \sqrt{2})}{ {3}^{2} -( { \sqrt{2} )}^{2} }$

$\frac{4(3 + \sqrt{2}) - \sqrt{5}(3 + \sqrt{2} ) }{9 - 2}$

$\frac{12 + 4 \sqrt{2} - 3 \sqrt{5} - \sqrt{10} }{7}$

Therefore, Required answer is 12+4√2-3√5-√10/7.