How do you simplify $\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} + \sqrt{5}}$ $(sqrt10 - sqrt 5) /( sqrt 10 + sqrt 5)$ ?

Question

How do you simplify $\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} + \sqrt{5}}$ $(sqrt10 - sqrt 5) /( sqrt 10 + sqrt 5)$ ?

1 Answer

Impact of this question

6027 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-11T17:00:14

$= 3 - 2 \sqrt{2}$ $=3-2sqrt2$

Explanation:

$\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} + \sqrt{5}}$ $(sqrt10-sqrt5)/(sqrt10+sqrt5)$
Multiplying both the sides by $\sqrt{10} - \sqrt{5}$ $sqrt(10)-sqrt(5)$
We get
$\frac{{(\sqrt{10} - \sqrt{5})}^{2}}{(\sqrt{10} + \sqrt{5}) (\sqrt{10} - \sqrt{5})}$ $(sqrt10-sqrt5)^2/((sqrt10+sqrt5)(sqrt10-sqrt5))$
$= \frac{10 + 5 - 2 \times \sqrt{10} \times \sqrt{5}}{10 - 5}$ $=(10+5-2timessqrt10timessqrt5)/(10-5)$
$= \frac{15 - 10 \sqrt{2}}{5}$ $=(15-10sqrt2)/5$
$= 5 \frac{3 - 2 \sqrt{2}}{5}$ $=5(3-2sqrt2)/5$
$= 3 - 2 \sqrt{2}$ $=3-2sqrt2$

Science

Math

Humanities

... and beyond

How do you simplify $\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} + \sqrt{5}}$ $(sqrt10 - sqrt 5) /( sqrt 10 + sqrt 5)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify √10−√5√10+√5(sqrt10 - sqrt 5) /( sqrt 10 + sqrt 5)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify $\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} + \sqrt{5}}$ $(sqrt10 - sqrt 5) /( sqrt 10 + sqrt 5)$ ?