How do you rationalize the denominator and simplify #sqrt (33/77)#?

Question

Abigail Allen · Accepted Answer

#sqrt(21)/7# #1#. Since the denominator of the fraction contains a radical, start by multiplying the numerator and denominator by #sqrt(77)/sqrt(77)#. Note that #sqrt(77)/sqrt(77)=1#, so that value of the fraction remains the same. #sqrt(33)/sqrt(77)# #=sqrt(33)/sqrt(77)(sqrt(77)/sqrt(77))# #2#. Simplify. #=sqrt(33*77)/77# #=sqrt(2541)/77# #3#. Use a perfect square to break down the radical in the numerator. #=sqrt(11^2*21)/77# #4#. Simplify. #=(11sqrt(21))/77# #=(color(red)cancelcolor(black)11^1sqrt(21))/color(red)cancelcolor(black)77^7# #=color(green)(|bar(ul(color(white)(a/a)sqrt(21)/7color(white)(a/a)|)))#

Hazel Anglin · Answer

undefined To rationalize the denominator and simplify √(33/77), we can follow these steps:

1. Simplify the fraction: 33/77 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 11. This gives us 3/7.

2. Rationalize the denominator: To rationalize the denominator, we need to eliminate any square roots from it. In this case, the denominator is 7. We can multiply both the numerator and denominator by √7 to get (√7 * 3)/(√7 * 7).

3. Simplify the expression: (√7 * 3)/(√7 * 7) can be further simplified by canceling out the common factor of √7 in the numerator and denominator. This leaves us with 3/7√7.

Therefore, the rationalized form of √(33/77) is 3/7√7.