How do you simplify 5 square root of 243?

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Answer 1 · 2018-03-20T02:11:48

The simplified radical is $45sqrt(3)$ .

First, we need to write the English statement in "math form":

$overbrace"5"^(5xx) overbrace"square root of"^(sqrtcolor(white)x) overbrace"243"^(quad243quad)$

To simplify this, factor $243$ into some square numbers that we know:

$color(white)=5xxsqrt243$

$=5xxsqrt(color(red)81*3)$

$=5xxsqrt(color(red)(9^2)*3)$

$=5xxcolor(red)9xxsqrt(3)$

$=45xxsqrt(3)$

$=45sqrt(3)$

This is the simplified radical. Hope this helped!