Question

Express 3.15 + 573 in the form m/5 + n √3 where m and n are rational numbers.

a) 120/5 + 101 √3
b) 115/5 + 110 √3
c) 116/5 + 115 √3
d) 118/5 + 112 √3

Answer 1

To express 3.15 + 573 in the form m/5 + n√3, the rational part is 573/5 and the irrational part is -83/10√3.

Step-by-step explanation:

To express 3.15 + 573 in the form m/5 + n√3, we need to separate the rational and irrational parts of the sum.

The rational part is obtained by taking the whole number and dividing it by 5, which gives us 573/5.

The irrational part is found by subtracting the rational part from the original sum, which gives us 3.15 - 573/5 = 3.15 - 1146/10 = (31.5 - 114.6)/10 = -83.1/10.

So, the expression can be written as (573/5) - (831/10)√3. Simplifying further, we get (573/5) - (1662/20)√3 = 116/5 - 83/10√3.