Question

`sqrt(3) xx root(3)(9) xx root(6)(3^5)` = ______.

Options

• 3

• 3^1/2

• 9

• 18

Answer 1

`sqrt(3) xx root(3)(9) xx root(6)(3^5)` = 9.

Explanation:

We are given the expression:

`sqrt(3) xx root(3)(9) xx root(6)(3^5)`

Let’s break it down step by step.

Step 1: Simplify each part of the expression

1. First term: `sqrt(3)`

`sqrt(3) = 3^(1//2)`

2. Second term: `root(3)(9)`

9 = 3², so `root(3)(9) = root(3)(3^2) = 3^(2//3)`

3. Third term: `root(6)(3^5)`

`root(6)(3^5) = 3^(5//6)`

Step 2: Combine the exponents

Now, we multiply all three terms together:

`3^(1//2) xx 3^(2//3) xx 3^(5//6)`

Using the property of exponents `a^m xx a^n = a^(m + n)`, we add the exponents:

`1/2 + 2/3 + 5/6`

To add these fractions, let’s first find a common denominator.

The least common denominator of 2, 3 and 6 is 6. 

Rewrite each fraction with denominator 6:

`1/2 = 3/6, 2/3 = 4/6, 5/6 = 5/6`

Now, add the fractions:

`3/6 + 4/6 + 5/6 = 12/6 = 2`

Step 3: Final result

Thus, the expression simplifies to 3² = 9