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# How do I simplify: 1 divided by (4 + square root of 3)?

### 11 Answers

- la consoleLv 73 years agoFavorite Answer
= 1/(4 + √3) → when the denominator is like (a + √b), you multiply it by (a - √b), and you multiply the top too of course

= [1 * (4 - √3)] / [(4 + √3).(4 - √3)]

= (4 - √3) / [16 - 4√3 + 4√3 - 3]

= (4 - √3) / [16 - 3]

= (4 - √3)/13 ← no term with √ at the denominator

- PinkgreenLv 73 years ago
1/[4+sqr(3)]

=

1[4-sqr(3)]/(16-3)

(multiply both the numerator

& the denominator with

4-sqr(3))

=

[4-sqr(3)]/13

- MICHAEL KLv 73 years ago
1 / (4 + square root 3) =

1 / (4 + 1.73205) =

1 / 5.73205 =

0.174457654765747.

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- JohnathanLv 73 years ago
Rationalize the denominator by multiplying by its conjugate.

1 / (4 + sqrt(3))

= (4 - sqrt(3)) / (4 + sqrt(3))(4 - sqrt(3))

= (4 - sqrt(3)) / (16 - 3)

= (4 - sqrt(3)) / 13. Final.

- L. E. GantLv 73 years ago
= 1/(4 + sqrt(3))

= 1/(4 + sqrt(3)) * (4 - sqrt(3))/4 -sqrt(3))

=(4 -sqrt(3))/ ((4+sqrt(3))(4-sqrt(3)))

= (4-sqrt(3)) /(4^2 - (sqrt(3))^2)

= (4 - sqrt(3)) /(16 - 3)

= (4 - sqrt(3)/13

- roderick_youngLv 73 years ago
It's already in simplest terms, but if you mean to clear the denominator, multiply top and bottom by the conjugate of the denominator. The conjugate is the same thing that is already on the bottom, but with the sign changed for the square root part. So multiply top and bottom by (4 - sqrt(3)). The bottom will multiply out into an integer.