what is the simpliest form of the quotient.
4 sgrt 810 / 4 sgrt 2
To find the simplest form of the quotient 4√810 / 4√2, we can simplify each square root separately and then divide.
First, let's simplify 4√810:
√810 can be simplified by breaking it down into its prime factors: √(2 * 3^4 * 5).
Taking out pairs of prime factors, we get 3^2 * √2 * √5, which simplifies to 9√2√5.
Next, let's simplify 4√2:
There are no simplifications that can be made for √2, so it remains as it is.
Now we have 9√2√5 / 4√2. Since both terms have a √2, we can divide them:
(9√5 * √2) / 4√2 = (9/4)√(5/1) = (9/4)√5.
Therefore, the simplest form of the quotient 4√810 / 4√2 is (9/4)√5.
To find the simplest form of the quotient (division) of √810 by √2, we need to simplify the square roots and divide the numbers inside the square roots separately.
Step 1: Simplify the square roots individually:
√810 = √(9 * 90) = 3√90
√2 remains the same.
Step 2: Divide the numbers inside the square roots separately:
3√90 / √2 = (3 * √90) / (1 * √2)
= (3 * √(9 * 10)) / (√2)
= (3 * 3 * √10) / (√2)
= (9√10) / (√2)
Step 3: Rationalize the denominator by multiplying both the numerator and the denominator by √2:
[(9√10) / (√2)] * [(√2) / (√2)]
= (9√20) / 2
So, the simplest form of the quotient 4√810 / 4√2 is (9√20) / 2.
4√810 / (4√2)
= √810 / √2
= √405