How do you rationalize the denominator and simplify #sqrt(49/10)#?

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Answer 1 · 2016-04-06T03:03:43

#(7sqrt10)/10#

#color(blue)(sqrt(49/10)#

Remember #color(brown)(sqrt(x/y)=sqrtx/sqrty#

So,

#rarrsqrt(49/10)=sqrt49/sqrt10#

#rarr7/sqrt10#

But wait!,In mathematics generally:

The denominators of fraction are not irrational numbers (the

numbers that cannot be expressed in the form #x/y#). So,we need to

rationalize the denominator.

So,

Multiply the whole fraction with

#rarr7/sqrt10*sqrt10/sqrt10#

#color(green)(rArr=(7sqrt10)/10#