How do you simplify #sqrt(30/77)#?

Question

Ethan Adkins · Accepted Answer

#sqrt(30/77)=color(blue)(sqrt(2310)/77#

Simplify:

#sqrt(30/77)#

Simplify.

#sqrt30/sqrt77#

Rationalize the denominator by multiplying the numerator and denominator by #sqrt77#.

#(sqrt30sqrt77)/(sqrt77sqrt77)#

Simplify. #(sqrt30sqrt77)/77#

Multiply #sqrt30xxsqrt77#.

#sqrt(2310)/77#

Eva Abramson · Answer

undefined To simplify sqrt(30/77), we can first simplify the fraction inside the square root. The square root of 30 can be simplified as sqrt(30) = sqrt(6 * 5) = sqrt(6) * sqrt(5). Similarly, the square root of 77 can be simplified as sqrt(77) = sqrt(7 * 11) = sqrt(7) * sqrt(11).

Therefore, sqrt(30/77) = (sqrt(6) * sqrt(5)) / (sqrt(7) * sqrt(11)).

Next, we can simplify the expression further by rationalizing the denominator. To do this, we multiply both the numerator and denominator by sqrt(7) * sqrt(11).

This gives us sqrt(30/77) = (sqrt(6) * sqrt(5) * sqrt(7) * sqrt(11)) / (sqrt(7) * sqrt(11) * sqrt(7) * sqrt(11)).

Simplifying further, we get sqrt(30/77) = (sqrt(6 * 5 * 7 * 11)) / (sqrt(7 * 11 * 7 * 11)).

Finally, simplifying the expression inside the square root, we have sqrt(30/77) = sqrt(2310) / sqrt(539).

Therefore, sqrt(30/77) simplifies to sqrt(2310) / sqrt(539).