Question

`(3/7)/(7√(10)/2 )`How do I simplify this problem? I have radical in the denominator and a fraction in the numerator.

Answer 1

Multiply the numerator and denominator by 7×2 = 14 to eliminate the denominators of those fractions:

`\frac{\frac37}{\frac{7√(10)}2}*(14)/(14)=(3*2)/(7√(10)*7)=\frac6{49√(10)}`

Rationalize the denominator by multiplying both numerator and denominator by √10:

`\frac6{49√(10)}*(√(10))/(√(10))=(6√(10))/(49(√(10))^2)=(6√(10))/(49*10)=(6√(10))/(490)`

Lastly, cancel the common factor of 2 in both the numerator and denominator (which comes from 6 = 2×3 and 490 = 2×245):

`(6√(10))/(490)=(3√(10))/(245)}`