Rationalize and simplify

Hi Tony :)

7 (sqrt (10))  (sqrt (14) ) ) / (6 (sqrt (35) ) )

\(\frac{7 \sqrt {10} \sqrt {14}}{6 \sqrt {35} }\\ =\frac{7\sqrt{2} \sqrt {5} \sqrt {2}\sqrt{7}}{6 \sqrt {5}\sqrt{7} }\\ =\frac{7\sqrt{2} \sqrt {2}}{6 }\\ =\frac{7*2}{6 }\\ =\frac{7}{3 }\\ =2\frac{1}{3}\)

Simplify the following:
(7 sqrt(10) sqrt(14))/(6 sqrt(35))

sqrt(10) sqrt(14) = sqrt(10×14):
(7 sqrt(10×14))/(6 sqrt(35))

10×14 = 140:
(7 sqrt(140 ) )/(6 sqrt(35))

sqrt(140) = sqrt(2^2×35) = 2 sqrt(35):
(7×2 sqrt(35))/(6 sqrt(35))

(7×2 sqrt(35))/(6 sqrt(35)) = (sqrt(35))/(sqrt(35))×(7×2)/6 = (7×2)/6:
(7×2)/6

2/6 = 2/(2×3) = 1/3:
Answer: |7/3

Yet ANOTHER aproach

7 (sqrt(10)(sqrt(14)  / (6 sqrt (35)

=  7 sqrt(140) / 6 sqrt(35)

=7 sqrt(4) / 6 = 7*2 /6 = 14/6 = 7/3