How do you rationalize the denominator and simplify #8/sqrt2#?

1 Answer
Jim G.
Aug 12, 2016

#4sqrt2#

Explanation:

#color(blue)"Rationalising"# the denominator means 'removing' the radical from the denominator and leaving a rational value in it's place.

To do this we make use of the following fact.

#color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtaxxsqrta=a)color(white)(a/a)|)))#

#rArrsqrt2xxsqrt2=2" a rational number"#

Since this is a fraction we must also multiply the numerator by #sqrt2#

#rArr8/sqrt2=8/sqrt2 xx(sqrt2)/(sqrt2)#

#=(8sqrt2)/2=(cancel(8)^4 sqrt2)/cancel(2)^1=4sqrt2" in simplest form"#

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