How do you simplify $\frac{6 \sqrt{20}}{3 \sqrt{5}}$ $(6sqrt20)/(3sqrt5)$ ?

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Answer 1 · 2015-11-12T06:44:12

$= 4$ $=color(blue)(4$

$\frac{6 \sqrt{20}}{3 \sqrt{5}}$ $(6sqrt(20))/(3sqrt5)$

Here, we first simplify $\sqrt{20}$ $sqrt20$ , by prime factorising $20$ $20$

$\sqrt{20} = \sqrt{5 \cdot 2 \cdot 2} = \sqrt{5 \cdot 2^{2}} = 2 \sqrt{5}$ $sqrt20=sqrt(5*2*2)=sqrt(5*2^2) = color(blue)(2sqrt5$

The expression now becomes:

$\frac{6 \sqrt{20}}{3 \sqrt{5}} = \frac{6 \cdot 2 \sqrt{5}}{3 \sqrt{5}}$ $(6sqrt(20))/(3sqrt5) =( 6* color(blue)(2sqrt5))/(3sqrt5)$

$= \frac{12 (\sqrt{5})}{3 \sqrt{5}}$ $=( 12(sqrt5))/(3sqrt5)$

$=( cancel12(cancelsqrt5))/(cancel3cancelsqrt5)$

$=color(blue)(4$

Answer 2 · 2015-11-12T06:46:35

$4$

Let's get the radical out of the denominator by doing the following:

$(6sqrt20)/(3sqrt5) * sqrt5/sqrt5$

$(6sqrt20* sqrt5)/(3*5)$

Now we can combine the roots like so:

$(6sqrt100)/(15)$

Now clean it up:

$(2sqrt100)/(5)$

$(2* 10)/(5)$

$(2* 2)/(1)$

$4$

How do you simplify (6sqrt20)/(3sqrt5)6√203√5(6sqrt20)/(3sqrt5)?