Question

Rationalize denominator

Answer 1

Option D. 2

Explanation:

Hello!

To rationalize the denominator, we should multiply the numerator and the denominator by the conjugate of the denominator. The conjugate simply means the same terms but with the opposite operation.

Rationalize

• 
  `\frac4{3+\sqrt7}`
• 
  `\frac4{3+\sqrt7} * (3 - \sqrt7)/(3 - \sqrt7)`
• 
  `(12 - 4\sqrt7)/(9 - 7)`
• 
  `(12 - 4\sqrt7)/(2)`

The new denominator is 2.

Answer 2

`\huge\boxed{\bf\:2}`

Explanation:

`(4)/(3 + √(7))`

Rationalise the denominator by multiplying the numerator & denominator of the fraction with
`(3 - √(7))`.

`(4\left(3-√(7)\right))/(\left(3+√(7)\right)\left(3-√(7)\right))`

Now, we an see that the denominator is in the form of the algebraic identity: (x + y) (x - y) = x² - y². So,

`(4\left(3-√(7)\right))/(3^(2)-\left(√(7)\right)^(2)) \\= (4\left(3-√(7)\right))/(9-7) \\= (4\left(3-√(7)\right))/(2) \\`

The new denominator is 2.

`\rule{150pt}{2pt}`