How do you rationalize the denominator and simplify $\frac{- \sqrt{3}}{\sqrt{2} + 5}$ $(-sqrt3)/ (sqrt 2 + 5)$ ?

Question

How do you rationalize the denominator and simplify $\frac{- \sqrt{3}}{\sqrt{2} + 5}$ $(-sqrt3)/ (sqrt 2 + 5)$ ?

1 Answer

Impact of this question

1287 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-08T20:00:18

See a solution process below:

Explanation:

To rationalize the denominator we need to multiply it by the appropriate form of $1$ $1$ . For this form of denominator we use this rule of quadratics to determine what to multiply by:

$(x + y) (x - y) = x^{2} - y^{2}$ $(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2$

$\frac{\sqrt{2} - 5}{\sqrt{2} - 5} \times \frac{- 3}{\sqrt{2} + 5} \Rightarrow$ $(sqrt(color(red)(2)) - color(blue)(5))/(sqrt(color(red)(2)) - color(blue)(5)) xx (-3)/(sqrt(color(red)(2)) + color(blue)(5)) =>$

$\frac{- 3 (\sqrt{2} - 5)}{{\sqrt{2}}^{2} - 5^{2}} \Rightarrow$ $(-3(sqrt(color(red)(2)) - color(blue)(5)))/(sqrt(color(red)(2))^2 - color(blue)(5)^2) =>$

$\frac{(- 3 \times \sqrt{2}) - (- 3 \times 5)}{2 - 25} \Rightarrow$ $( (-3 xx sqrt(color(red)(2))) - (-3 xx color(blue)(5)))/(2 -25) =>$

$\frac{- 3 \sqrt{2} - (- 15)}{2 - 25} \Rightarrow$ $(-3sqrt(2) - (-15))/(2 -25) =>$

$\frac{- 3 \sqrt{2} + 15}{- 23} \Rightarrow$ $(-3sqrt(2) + 15)/(-23) =>$

$- \frac{15 - 3 \sqrt{2}}{23}$ $-(15 - 3sqrt(2))/23$

Science

Math

Humanities

... and beyond

How do you rationalize the denominator and simplify $\frac{- \sqrt{3}}{\sqrt{2} + 5}$ $(-sqrt3)/ (sqrt 2 + 5)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you rationalize the denominator and simplify −√3√2+5(-sqrt3)/ (sqrt 2 + 5)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you rationalize the denominator and simplify $\frac{- \sqrt{3}}{\sqrt{2} + 5}$ $(-sqrt3)/ (sqrt 2 + 5)$ ?