How do you rationalize the denominator and simplify $\frac{5 \sqrt{6}}{\sqrt{10}}$ $(5sqrt6)/sqrt10$ ?

Question

How do you rationalize the denominator and simplify $\frac{5 \sqrt{6}}{\sqrt{10}}$ $(5sqrt6)/sqrt10$ ?

3 Answers

Impact of this question

3353 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-09T20:44:47

$\sqrt{15}$ $sqrt15$

Explanation:

multiply by $\sqrt{10}$ $sqrt10$ :

$\frac{5 \sqrt{6} \sqrt{10}}{{(\sqrt{10})}^{2}}$ $(5sqrt6sqrt10)/((sqrt10)^2)$

$\sqrt{6} \cdot \sqrt{10} = \sqrt{6 \cdot 10} = \sqrt{60}$ $sqrt6 * sqrt10 = sqrt (6*10) = sqrt60$

${(\sqrt{10})}^{2} = 10$ $(sqrt10)^2 = 10$

$\frac{5 \sqrt{6}}{\sqrt{10}} = \frac{5 \sqrt{60}}{10}$ $(5sqrt6)/(sqrt10) = (5sqrt60)/10$

$\sqrt{60} = \sqrt{4} \cdot \sqrt{15} = 2 \sqrt{15}$ $sqrt60 = sqrt4 * sqrt15 = 2sqrt15$

$5 \sqrt{60} = 5 \cdot 2 \cdot \sqrt{15} = 10 \sqrt{15}$ $5sqrt60 = 5 * 2 * sqrt15 = 10sqrt15$

$\frac{5 \sqrt{60}}{10} = \frac{10 \sqrt{15}}{10}$ $(5sqrt60)/10 = (10sqrt15)/10$

$= \frac{\sqrt{15}}{1}$ $= (sqrt15)/1$

$= \sqrt{15}$ $= sqrt15$

Answer 2 · 2018-03-09T20:53:14

$\sqrt{15}$ $sqrt15$

Explanation:

In order to rationalize the denominator, you can multiply by $\frac{\sqrt{10}}{\sqrt{10}}$ $sqrt10/sqrt10$ . This is the same as multiplying the fraction by one. If you multiply $\frac{5 \sqrt{6}}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$ $(5sqrt6)/sqrt10 *sqrt10/sqrt10$ , you get $\frac{5 \sqrt{60}}{10}$ $(5sqrt60)/10$ . If you multiply the square roots in the denominator, you get $\sqrt{100}$ $sqrt100$ , which is equivalent to 10.

With $\frac{5 \sqrt{60}}{10}$ $(5sqrt60)/10$ , you can simplify to just $\frac{\sqrt{60}}{2}$ $sqrt60/2$ .

Next, you can simplify $\sqrt{60}$ $sqrt60$ by doing a factor tree. When you do a factor tree, you will find you can pull out a factor of 2 from the square root leaving you with $\frac{2 \sqrt{15}}{2}$ $(2sqrt15)/2$ .

Lastly, just cancel out the 2 in the numerator and denominator, and you get the answer of $\sqrt{15}$ $sqrt15$

Answer 3 · 2018-03-09T20:55:00

$\sqrt{15}$ $sqrt15$

Explanation:

$using the laws of radicals$ $"using the "color(blue)"laws of radicals"$

$∙ x \sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a} b$ $•color(white)(x)sqrtaxxsqrtbhArrsqrtab$

$∙ x \sqrt{a} \times \sqrt{a} = a$ $•color(white)(x)sqrtaxxsqrta=a$

$To rationalise the denominator that is eliminate the$ $"To rationalise the denominator that is eliminate the "$
$radical from the denominator$ $"radical from the denominator"$

$multiply numerator/denominator by \sqrt{10}$ $"multiply numerator/denominator by "sqrt10$

$\Rightarrow \frac{5 \sqrt{6}}{\sqrt{10}}$ $rArr(5sqrt6)/sqrt10$

$= \frac{5 \times \sqrt{6} \times \sqrt{10}}{\sqrt{10} \times \sqrt{10}}$ $=(5xxsqrt6xxsqrt10)/(sqrt10xxsqrt10)$

$= \frac{5 \times \sqrt{60}}{10}$ $=(5xxsqrt60)/10$

$= \frac{5 \times \sqrt{4 \times 15}}{10}$ $=(5xxsqrt(4xx15))/10$

$= \frac{5 \times \sqrt{4} \times \sqrt{15}}{10}$ $=(5xxsqrt4xxsqrt15)/10$

$=(5xx2xxsqrt15)/10=(cancel(10)sqrt15)/cancel(10)=sqrt15$

Science

Math

Humanities

... and beyond

How do you rationalize the denominator and simplify $\frac{5 \sqrt{6}}{\sqrt{10}}$ $(5sqrt6)/sqrt10$ ?

3 Answers

Explanation:

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you rationalize the denominator and simplify (5sqrt6)/sqrt105√6√10(5sqrt6)/sqrt10?

3 Answers

Explanation:

Explanation:

Explanation:

Related questions

Impact of this question

How do you rationalize the denominator and simplify $\frac{5 \sqrt{6}}{\sqrt{10}}$ $(5sqrt6)/sqrt10$ ?