Question

pllzzz simplify all the three points by rationalizing rhe denominator.....
whoevwr will correctly answer the que will be marked brainliest by mee...
but check ur answer before posting​

Answer 1

Answer:

Step-by-step explanation:

(i) Multiply both the numerator and the denominator of the number with   the conjugate of the denominator(7 - 3 root5)

The conjugate of the denominator 7 - 3 root5 is 7 + 3 root5

That is,

= 7 + 3 root5/7 - 3 root5 X 7 + 3 root5/7 + 3 root5

Now,

Follow the identity

= 7^2 + 2(7)(3 root5) + (3 root5)^2[using identity (a + b)^2 = a^2 + 2ab + b^2]/7^2 - (3 root5)^2[using identity a^2 - b^2 = (a + b)(a - b)]

= 49 + 48 root5 + 45/49 - 45

= 49 + 45 + 48 root5/4

= 94 + 42 root5/4

= 47 + 21 root5/2

(ii) Multiply both the numerator and the denominator of the number with   the conjugate of the denominator(2 root2 + 3 root3)

The conjugate of the denominator 2 root2 + 3 root3 is 2 root2 - 3 root3

That is,

= 2 root3 - root5/2 root2 + 3 root3 X 2 root2 - 3 root3/2 root2 - 3 root3

Now,

Follow the identity

= (2 root3 + root5)(2 root2 - 3 root3)/(2 root2)^2 - (3 root3)^2[using  identity a^2 - b^2 = (a + b)(a - b)]

= 2 root 3 X 2 root2 - 2 root3 X 3 root3 + root5 X 2 root2 - root5 X 3 root3[using distributive property of multiplication]/4 X 2 - 9 X 3

= 4 root6 - 6 root9 + 2 root10 - 3 root15/8 - 27

= 4 root6 - 6 X 3(3^2 = 9) + 2 root10 - 3 root15/-19

= 4 root6 -18 + 2 root10 - 3 root15/-19

Make the denominator's sign positive

= - (4 root6 -18 + 2 root10 - 3 root15)/19

= - 4 root6 + 18 - 2 root10 + 3 root15/19

(iii) Multiply both the numerator and the denominator of the number with   the conjugate of the denominator(root48 + root18)

The conjugate of the denominator root48 + root18 is root48 - root18

That is,

= 7 root3 - 5 root2/root48 + root18 X root48 - root18/root48 - root18

Now,

Follow the identity

= (7 root3 - 5 root2)(root48 - root18)/(root48)^2 - (root18)^2[using  identity a^2 - b^2 = (a + b)(a - b)]

= 7 root3 X root48 - 7 root3 X root18 - 5 root2 X root48 + 5 root2 X root18[using distributive property of multiplication]/48(root48^2 = 48) - 18(root18^2 = 18)

= 7 root144 - 7 root54 - 5 root96 + 5 root36/30

= 7 X 12(12^2 = 144) + 5 X 6(6^2 = 36) - 7 root54 - 5 root96/30

= 84 + 30 - 7 root54 - 5 root96/30

= 114 - 7 root54 + 5 root96/30

Answer 2

Given :   (7 + 3√5) / ( 7 - 3√5) ,   (2√3  -  √5)/(2√2 + 3√3)

To find :  rationalizing the denominator.....

Solution:

(7 + 3√5) / ( 7 - 3√5)

multiplying numerator & denominator by 7 + 3√5

= (7 + 3√5) (7 + 3√5)  / (7 - 3√5) (7 + 3√5)

= ( 49 + 45 + 42√5)/(49 - 45)

= (94 +  42√5)/(4)

= (47 + 21√5)/2

(2√3  -  √5)/(2√2 + 3√3)

multiplying numerator & denominator by  3√3 - 2√2

(2√3  -  √5) ( 3√3 - 2√2) / (2√2 + 3√3) ( 3√3 - 2√2)

= ( 18 + 2√10 - 4√6 - 3√15)/(27  - 8)

= ( 18 + 2√10 - 4√6 - 3√15)/19

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