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Rationalize the denominator. 12/(4sqrt3 - sqrt 2) - Algebra

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प्रश्न

Rationalize the denominator.

`12/(4sqrt3 - sqrt 2)`

योग
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उत्तर

`12/(4sqrt3 - sqrt 2)`

`= 12/(4sqrt3 - sqrt 2) xx  (4sqrt3 + sqrt 2)/(4sqrt3 + sqrt 2)`

`= (12 (4sqrt3 + sqrt 2))/((4sqrt3)^2 -(sqrt 2)^2)   ...[(a+b)(a-b) = a^2 - b^2]`

`=(12 (4sqrt3 + sqrt 2))/(48 - 2)`

`= (12 (4sqrt3 + sqrt 2))/46`

`= (6 (4sqrt3 + sqrt 2))/23`

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Simplifying an Expression by Rationalization of the Denominator
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Real Numbers - Problem Set 2 [पृष्ठ ३५]

APPEARS IN

बालभारती Mathematics 1 [English] Standard 9 Maharashtra State Board
अध्याय 2 Real Numbers
Problem Set 2 | Q (8) (v) | पृष्ठ ३५

संबंधित प्रश्न

Rationalize the denominator.

`3/(2 sqrt 5 - 3 sqrt 2)`


Rationalise the denominators of:

`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`


Simplify:

`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`


Rationalise the denominator of `1/[ √3 - √2 + 1]`


Simplify by rationalising the denominator in the following.

`(2)/(3 + sqrt(7)`


Simplify by rationalising the denominator in the following.

`(4 + sqrt(8))/(4 - sqrt(8)`


Simplify the following :

`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`


In the following, find the values of a and b:

`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`


In the following, find the values of a and b:

`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`


In the following, find the value of a and b:

`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`


If x = `(7 + 4sqrt(3))`, find the value of

`sqrt(x) + (1)/(sqrt(x)`


If x = `(7 + 4sqrt(3))`, find the value of

`x^2 + (1)/x^2`


If x = `(4 - sqrt(15))`, find the values of 

`(1)/x`


If x = `(4 - sqrt(15))`, find the values of 

`x^2 + (1)/x^2`


If x = `(4 - sqrt(15))`, find the values of

`x^3 + (1)/x^3`


If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of

x2 + y2


If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of 

x3 + y3


If x = `sqrt3 - sqrt2`, find the value of:

(i) `x + 1/x`

(ii) `x^2 + 1/x^2`

(iii) `x^3 + 1/x^3`

(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`


Show that:

`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`


Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`


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