divide 15√54/3√2
To divide the expression 15√54 by 3√2, we can simplify each square root separately before performing the division.
First, simplify the square roots:
√54 = √(9 * 6) = √9 * √6 = 3√6
√2 remains the same.
Now we can rewrite the expression as:
(15 * 3√6) / (3√2)
Since the square roots in the numerator and denominator are the same (both have √6 and √2), we can cancel them out:
(15 * 3√6) / (3√2) = (15 * 3) / 1 = 45
Therefore, 15√54 divided by 3√2 equals 45.
To divide the expression (15√54) by (3√2), we can use the rule of division of radicals.
Step 1: Simplify the expression under the radical sign separately.
√54 can be simplified by factoring it into its prime factors:
√54 = √(2 * 3^3) = √(2 * 3 * 3 * 3)
= 3√2
Step 2: Rewrite the expression using the simplified radical form.
15√54 = 15 * 3√2 = 45√2
Step 3: Divide the expressions outside the radical sign.
45√2 / 3√2
Since the expressions inside the radical signs are the same (both 2), we can simplify it.
45√2 / 3√2 = 45/3 = 15
Therefore, the simplified result is 15.
To divide 15√54 by 3√2, we can simplify the square roots and the whole numbers separately.
Let's start by simplifying the square roots:
√54 can be simplified by splitting it into prime factors. 54 = 2 * 3^3. We can simplify the square root further: √54 = √(2 * 3^3) = 3√2.
Now, let's simplify the whole numbers:
15 = 3 * 5.
Combining the simplified square roots and the whole numbers, we get:
15√54 = 3 * 5 * 3√2 = 15 * 3√2 = 45√2.
Therefore, 15√54 divided by 3√2 equals 45√2.