Question

Rationalize the denominator
2/5+3root2​

Answer 1

Answer:

5−325+32=a+b25−325+32×5+325+32=a+b252−(3)2(5+32)=a+b225−325+3+103=a+b22228+103=a+b2a=2228andb=2210a=1114andb=115

Answer 2

Answer:

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

6

−

15

=

13

(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