what is the square root of 5 divided by 2 times the square root of 125?
To solve this equation, we first need to simplify it step by step.
Let's start by simplifying the expression inside the bracket:
√5 ÷ 2 * √125
Step 1: Simplify the square root of 5:
The square root of 5 is an irrational number. However, we can express it as √5.
Step 2: Simplify the square root of 125:
The square root of 125 can be simplified as follows:
√125 = √(5^2 * 5) = 5√5
Now, we have:
√5 ÷ 2 * 5√5
Next, let's simplify the division:
√5 ÷ 2 = (√5 * 1) ÷ 2 = (√5/2)
Now, we have:
(√5/2) * 5√5
To simplify further, we can multiply across:
(√5/2) * 5√5 = (5/2) * (√5 * √5) = (5/2) * 5 = 25/2
Therefore, the square root of 5 divided by 2 times the square root of 125 equals 25/2.