1.

Rasonalize :- 2√3-3√2 / 3√2+2√3​

Answer»

Answer:

5-2√6

5-2√6_____

5-2√6_____5

Step-by-step explanation:

2√3 - 3√2

________

3√2 + 2√3

also, it is EQUAL to

2√3 - 3√2

________

2√3 + 3√2

rationalising numerator

(2√3-3√2) (2√3-3√2) { (a-b)² }

_________________

(2√3+3√2) (2√3-3√2) { (a+b)(a-b) }

where a = 2√3,

b = 3√2

so,

(2√3-3√2)²

_________

(2√3)² + (3√2)²

(2√3)² + (3√2)² - 2 (2√3)(3√2)

_______________________

4 × 3 + 9 ×2

12 + 18 - 12√6

___________

12 + 18

30-12√6

_______

30

6(5 - 2√6)

________

6(5)

6 gets cancelled

so,

5-2√6

_____

5


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