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Rationalise the denominator and simplify      10

                                                                          3sqrt5

Guest Feb 18, 2017

Best Answer 

 #6
avatar+26236 
+15

Perhaps I should have included the following extra step:

 

 \(\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times\sqrt5\times\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}etc\)

 

i.e. you multiply the expression by 1 in the form \(\frac{\sqrt5}{\sqrt5}\)  Then you multiply the two \(\sqrt5\)s on the bottom together.

 

Hope this explains it adequately for you.

.

Alan  Feb 18, 2017
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8+0 Answers

 #1
avatar+186 
0

10/3sqrt5

 

(10/3)/((3sqrt5)/3)=

3.33/sqrt5

 

3.332/sqrt52=

11.11/5

 

11.11/5=20/9 so

 

10/3sqrt5=20/9

Scruffy23.  Feb 18, 2017
 #2
avatar+186 
0

wait i checked with calculator and this is wrong so i dont know where i slipped up

Scruffy23.  Feb 18, 2017
 #8
avatar+6810 
+5

You did this: 

\(\dfrac{3.33^2}{\sqrt5^2}\)

But you should take a square root after squaring both numerator and denominator......

Correct answer:

\(\sqrt{\dfrac{3.33^2}{\sqrt5^2}}\\ =\sqrt{\dfrac{100}{9}\cdot \dfrac{1}{5}}\\ =\sqrt{\dfrac{20}{9}}\\ =\dfrac{\sqrt{20}}{\sqrt9}\\ =\dfrac{\sqrt{20}}{3}\)

 

And knowing that \(\sqrt{20}=\sqrt{2^2\cdot 5}=2\sqrt 5\)

 

Final answer = \(\dfrac{2}{3}\sqrt 5\)

MaxWong  Feb 18, 2017
 #3
avatar+26236 
+5

Like so:  \(\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}\rightarrow\frac{2\sqrt5}{3}\)

 

.

Alan  Feb 18, 2017
 #4
avatar+90563 
+3

Hi Alan :))

Melody  Feb 18, 2017
 #7
avatar+26236 
+3

Hi Melody!

Alan  Feb 18, 2017
 #5
avatar
+5

How does the 3sqrt5 turn to 3*5?

Guest Feb 18, 2017
 #6
avatar+26236 
+15
Best Answer

Perhaps I should have included the following extra step:

 

 \(\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times\sqrt5\times\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}etc\)

 

i.e. you multiply the expression by 1 in the form \(\frac{\sqrt5}{\sqrt5}\)  Then you multiply the two \(\sqrt5\)s on the bottom together.

 

Hope this explains it adequately for you.

.

Alan  Feb 18, 2017

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