(60 + 16sqrt(15))/(60 + 17sqrt(15))
i tried dividing but got stuck thanks
To simplify the expression (60 + 16√15)/(60 + 17√15), we can use a technique called rationalizing the denominator. This involves multiplying the numerator and denominator by the conjugate of the denominator.
The conjugate of 60 + 17√15 is 60 - 17√15. To rationalize the denominator, we multiply both the numerator and denominator by the conjugate:
((60 + 16√15)/(60 + 17√15)) * ((60 - 17√15)/(60 - 17√15))
To simplify the denominator, we'll use the difference of squares rule, which states that (a + b)(a - b) = a^2 - b^2. In this case, a = 60 and b = 17√15:
((60 + 16√15)(60 - 17√15)) / ((60)^2 - (17√15)^2)
Simplifying the numerator and denominator further:
(3600 - 272√15 + 960√15 - (17√15)^2) / (3600 - 289*15)
Notice that the cross terms (those involving both √15 and the constant) cancel each other out:
(3600 - 272√15 + 960√15 - 17^2*15) / (3600 - 289*15)
Simplifying further:
(3600 + 688√15 - 15*289) / (3600 - 289*15)
Now, you can evaluate this expression using a calculator to get a decimal approximation.