Simplifying the expression: √24 / 8 √54 / 9

To simplify this expression, we will break it down step by step.

Step 1: Simplify the square roots individually.
√24 can be broken down as √(4 * 6). Since 4 is a perfect square (2 * 2 = 4), we can take it out of the square root. This gives us 2√6.
Similarly, √54 can be broken down as √(9 * 6). Taking out the perfect square 9, we get 3√6.

Step 2: Simplify the expression further by canceling out common factors.
We can cancel out the common factor of √6 from both the numerator and denominator.
So, the expression becomes (2/8) * (3/9).

Step 3: Simplify the fractions.
The fraction 2/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
2 ÷ 2 = 1 and 8 ÷ 2 = 4. So, 2/8 simplifies to 1/4.
Similarly, the fraction 3/9 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3.
3 ÷ 3 = 1 and 9 ÷ 3 = 3. So, 3/9 simplifies to 1/3.

Step 4: Multiply the simplified fractions.
Multiplying 1/4 and 1/3 gives us 1/12.

Therefore, the simplified expression is 1/12.

Root (24÷8) × root (54÷9)
=root (3) × root (6)
=root (18)