Question

Rationalize the denominator

$\bf \dfrac{√6}{√3+√2}$
​

Answer 1

Answer:

Root 6 = 36

Root 3 = 9

Root 2 = 4

36 divide / 9+4 = 13

so,

36/13

The answer is 2.7

Answer 2

Step-by-step explanation:

Given:

$\bf \dfrac{√6}{√3+√2}$

To find:Rationalize the denominator.

Solution:

Tip: Identity used in denominator

$\boxed{\bold{(x - y)(x + y) = {x}^{2} - {y}^{2} }}$

Step 1: Multiply and divide by rationalization factor

$\frac{ \sqrt{6} }{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} }$

Step 2: Apply identity in denominator

$= \frac{ \sqrt{6}( \sqrt{3} - \sqrt{2} ) }{( { \sqrt{3}) }^{2} - ( { \sqrt{2}) }^{2} }$

or

$= \frac{ \sqrt{6}( \sqrt{3} - \sqrt{2} ) }{3 - 2 }$

or

$= { \sqrt{6}( \sqrt{3} - \sqrt{2} ) }$

Step 3: Can simplify further by multiplying √6

$= \sqrt{6} \sqrt{3} - \sqrt{6} \sqrt{2}$

or

$= \sqrt{6 \times 3 } - \sqrt{6 \times 2}$

or

$= \sqrt{18} - \sqrt{12}$

or

$= \sqrt{9 \times 2} - \sqrt{4 \times 3}$

or

$= 3 \sqrt{2} - 2 \sqrt{3}$

Final answer:

$\bold{\frac{ \sqrt{6}}{( \sqrt{3} - \sqrt{2} )}= 3 \sqrt{2} - 2 \sqrt{3} }$

Hope it helps you.

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