Question

Express (3+√7). In the form a + √b
_____
(3-√2)

Answer 1

Answer:

 

Step-by-step explanation:

 Given Express (3+√7). In the form a + √b

_____

(3-√7)

By rationalizing the denominator we can take as

 3 + √7 / 3 - √7 x 3 + √7 / 3 - √7

 So we get

 (3 + √7)^2 / (3)^2 - (√7)^2

 This is in the form of a^2 - b^2 = (a + b)(a - b)

  (3 + √7)^2 / 9 - 7

 9 + 7 + 6√7 / 2

 16 + 6√7 / 2

8 + 3√7

This is of the form a + √b

Answer 2

 

We will first rationalize the expression,

 3 + √7 / 3 - √7 x 3 + √7 / 3 - √7

= (3 + √7)^2 / (3)^2 - (√7)^2      {Since we know, a^2 - b^2 = (a + b)(a - b)}

 = (3 + √7)^2 / 9 - 7

= 9 + 7 + 6√7 / 2

 = 16 + 6√7 / 2

=  8 + 3√7

hence, (8 + 3√7) is the right answer to the given equation.

Hope it helps!