# Simplifying Radical Expressions

##### New member
I sort of understand how to do this and sort of not. I like need an explanation of like each step cause I have more like this...

Example 1:

[sqrt(7)/sqrt(2)] times [sqrt(14)/sqrt(27)]

i think the next step is sqrt(98)/sqrt(54) and then i think you rationalize the denominator and get

sqrt(5292)/54

thankyou very very much for your help

#### daon

##### Senior Member
I sort of understand how to do this and sort of not. I like need an explanation of like each step cause I have more like this...

Example 1:

[sqrt(7)/sqrt(2)] times [sqrt(14)/sqrt(27)]

i think the next step is sqrt(98)/sqrt(54) and then i think you rationalize the denominator and get

sqrt(5292)/54

thankyou very very much for your help
$$\displaystyle \frac{\sqrt{7}}{\sqrt{2}}\frac{\sqrt{14}}{\sqrt{27}} = \sqrt{\frac{7*14}{2*27}} = \sqrt{\frac{98}{54}} = \sqrt{\frac{49*27}{27*27}} = \frac{7\sqrt{27}}{27} = \frac{7\sqrt{9*3}}{27} = \frac{21\sqrt{3}}{27} = \frac{7\sqrt{3}}{9}$$

##### New member
ok i have no idea where you got the sqrt (49*27) / (27*27)
i under stand everything up to there

#### daon

##### Senior Member
ok i have no idea where you got the sqrt (49*27) / (27*27)
i under stand everything up to there
Sorry, I accidently combined two steps into one..

$$\displaystyle \sqrt{\frac{98}{54}} = \sqrt{\frac{49}{27}} = \sqrt{\frac{49*27}{27*27}}$$

#### soroban

##### Elite Member
$$\displaystyle \L\,\sqrt{\frac{7}{2}}\,\cdot\,\sqrt{\frac{14}{27}}$$
$$\displaystyle \L\;\;\sqrt{\frac{7\cdot14}{2\cdot27}}\;=\;\sqrt{\frac{7\cdot7\cdot\not{2}}{\not{2}\cdot9\cdot3}} \;= \;\sqrt{\frac{49}{9\cdot3}} \;=\;\frac{\sqrt{49}}{\sqrt{9}\cdot\sqrt{3}}\;=\;\frac{7}{3\sqrt{3}}$$
Rationalize the denominator: $$\displaystyle \L\:\frac{7}{3\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}\;=\;\frac{7\sqrt{3}}{9}$$