How do you simplify $\frac{5 \sqrt{10} + 9 \sqrt{3}}{3 \sqrt{6}}$ $(5sqrt10+9sqrt3)/(3sqrt6)$ ?

Question

How do you simplify $\frac{5 \sqrt{10} + 9 \sqrt{3}}{3 \sqrt{6}}$ $(5sqrt10+9sqrt3)/(3sqrt6)$ ?

1 Answer

Impact of this question

1065 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-02T19:27:51

$\frac{5 \sqrt{15}}{9} + \frac{3 \sqrt{2}}{2}$ $(5sqrt(15))/9+(3sqrt(2))/2$

Explanation:

Write as:

$\frac{5 \sqrt{10}}{3 \sqrt{6}} + \frac{9 \sqrt{3}}{3 \sqrt{6}}$ $(5sqrt(10))/(3sqrt(6))+(9sqrt(3))/(3sqrt(6))$

$= \frac{5 \sqrt{10} + 9 \sqrt{3}}{3 \sqrt{6}}$ $=(5sqrt(10)+9sqrt(3))/(3sqrt(6))$

Getting rid of the root in the denominator

$= \frac{5 \sqrt{10} + 9 \sqrt{3}}{3 \sqrt{6}} \times 1 \to \frac{5 \sqrt{10} + 9 \sqrt{3}}{3 \sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}$ $color(green)(=(5sqrt(10)+9sqrt(3))/(3sqrt(6))color(red)(xx1)" "->" "(5sqrt(10)+9sqrt(3))/(3sqrt(6))color(red)(xx(sqrt(6))/(sqrt(6))))"$

$\frac{5 \sqrt{10 \times 6} + 9 \sqrt{3 \times 6}}{3 {(\sqrt{6})}^{2}}$ $" "color(green)((5sqrt(10xx6)+9sqrt(3xx6))/(3(sqrt(6))^2))$

$\frac{5 \sqrt{10 \times 6} + 9 \sqrt{3 \times 6}}{18}$ $" "color(green)((5sqrt(10xx6)+9sqrt(3xx6))/(18)$

$\frac{5 \sqrt{2 \times 5 \times 2 \times 3} + 9 \sqrt{3 \times 3 \times 2}}{18}$ $" "color(green)((5sqrt(2xx5xx2xx3)+9sqrt(3xx3xx2))/(18)$

$\frac{10 \sqrt{15} + 27 \sqrt{2}}{18}$ $" "color(green)((10sqrt(15)+27sqrt(2))/(18)$

$\frac{5 \sqrt{15}}{9} + \frac{3 \sqrt{2}}{2}$ $" "color(green)((5sqrt(15))/9+(3sqrt(2))/2)$

Science

Math

Humanities

... and beyond

How do you simplify $\frac{5 \sqrt{10} + 9 \sqrt{3}}{3 \sqrt{6}}$ $(5sqrt10+9sqrt3)/(3sqrt6)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify 5√10+9√33√6(5sqrt10+9sqrt3)/(3sqrt6)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify $\frac{5 \sqrt{10} + 9 \sqrt{3}}{3 \sqrt{6}}$ $(5sqrt10+9sqrt3)/(3sqrt6)$ ?