Divide 16√35 / 4√7
To divide 16√35 by 4√7, you divide the numbers outside of the square roots and then divide the numbers inside the square roots separately.
16 divided by 4 is 4.
√35 divided by √7 is √(35/7) which simplifies to √5.
Therefore, 16√35 / 4√7 is equal to 4√5.
To divide the expression (16√35) by (4√7), we can simplify the square root terms separately and then divide the numbers.
Let's start by simplifying the square root terms:
√35 can be broken down as √(5 * 7). Taking the square root of 5 and 7 individually, we get √5 * √7.
Next, let's simplify the numerator and denominator:
(16√35) = (16 * √5 * √7)
and
(4√7) = (4 * √7)
Now, we can rewrite the division expression as:
(16 * √5 * √7) / (4 * √7)
Since the denominator (4 * √7) is common to both terms in the numerator, we can cancel it out:
(16 * √5 * √7) / (4 * √7) = (16 * √5) / 4
Further simplifying, we can divide 16 by 4, which equals 4. Therefore, the final simplified answer is:
(16√35) / (4√7) = 4√5
To divide the given expression 16√35 / 4√7, we can simplify it step by step using the properties of radicals.
Step 1: Simplify the denominator by multiplying the entire expression by √7/√7, which is the same as multiplying by 1:
(16√35 / 4√7) * (√7/√7)
This gives us: (16√35 * √7) / (4 * √7 * √7)
Step 2: Simplify the expressions in the numerator and denominator:
(16 * √7 * √35) / (4 * √7 * √7)
Simplifying the square roots:
(16 * √(7 * 35)) / (4 * √(7^2))
Step 3: Simplify the expressions inside the square roots:
(16 * √(7 * 35)) / (4 * 7)
Simplifying further:
(16 * √(245)) / 28
Step 4: Divide the numerator by the denominator:
16 / 28 = 4/7
Therefore, the simplified form of the given expression 16√35 / 4√7 is 4/7.