Question

22 /√3 + 6 /√27 can be written as a√3
Find the value of a.

Answer 1

a=8

Explanation:

First make the denominators whole numbers.

22
`√(3)`/3 + 6
`√(27)`/27

Now make the denominators the same. To change 3 to 27, multiply by 9.

198
`√(3)`/27 + 6
`√(27)`/27

simplify6
`√(27)` which is 6
`√(9)`
`√(3)` simplified to 6 x 3
`√(3)`=18
`√(3)`

(198
`√(3)`+18
`√(3)`)/27

198 plus 18 is 216

216
`√(3)`/27

216 divided by 27 is 8

8
`√(3)`

8 is in the place of a in the equation a
`√(3)` so a = 8

Answer 2

Answer: To solve the expression 22 /√3 + 6 /√27, we need to rationalize the denominator of the second term. We can do this by multiplying both the numerator and denominator of the second term by √3. This gives us:

22 /√3 + 6 /√27

= 22 /√3 + 6 * √3 / (√3 * √3 * √3)

= 22 /√3 + 6 * √3 / 3√3

= 22 /√3 + 2√3

= (22 + 2)√3

= 24√3

Therefore, a = 24.