Question

A = √7 + √c and b = √63 + √d where c and d are positive integers.

Given that c: d = 1: 9
find, in its simplest form, the ratio a: b

Answer 1

`\displaystyle a:b=(1)/(3)`

Step-by-step explanation:

Ratios

We are given the following relations:

`a=√(7)+√(c)\qquad \qquad[1]`

`b=√(63)+√(d)\qquad \qquad[2]`

`\displaystyle (c)/(d)=(1)/(9) \qquad \qquad [3]`

From [3]:

`9c=d`

Replacing into [2]:

`b=√(63)+√(9c)`

We can express 63=9*7:

`b=√(9*7)+√(9c)`

Taking the square root of 9:

`b=3√(7)+3√(c)`

Factoring:

`b=3(√(7)+√(c))`

Find the ration a:b:

`\displaystyle a:b=(√(7)+√(c))/(3(√(7)+√(c)))`

Simplifying:

`\boxed{a:b=(1)/(3)}`