+0

# Rationalise the denominator and simplify 10

0
106
8

Rationalise the denominator and simplify      10

3sqrt5

Guest Feb 18, 2017

#6
+25984
+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
Sort:

#1
+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
+186
0

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

Scruffy23.  Feb 18, 2017
#8
+6765
+5

You did this:

$$\dfrac{3.33^2}{\sqrt5^2}$$

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

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

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
+25984
+5

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

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Alan  Feb 18, 2017
#4
+89775
+3

Hi Alan :))

Melody  Feb 18, 2017
#7
+25984
+3

Hi Melody!

Alan  Feb 18, 2017
#5
+5

How does the 3sqrt5 turn to 3*5?

Guest Feb 18, 2017
#6
+25984
+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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