Divide √60/2√5
To simplify this expression, we can divide both the numerator and the denominator individually.
√60/2√5 = (√60)/(2√5)
First, let's simplify the numerator:
√60 = √(4*15) = √4 * √15 = 2√15
Now, let's simplify the denominator:
2√5 = 2 * √5
Now, we can substitute these simplified expressions back into the main expression:
(2√15) / (2 * √5)
The 2's in the numerator and the denominator can cancel each other out:
(√15) / (√5)
Finally, we can rationalize the denominator by multiplying both the numerator and the denominator by √5:
(√15 * √5) / (√5 * √5)
This simplifies to:
√(15*5) / (√25)
The square root of 15 times 5 is the square root of 75, which can be simplified to:
√75 / 5
Therefore, √60/2√5 simplifies to √75/ 5.
To divide √60/2√5, we can simplify the expression as follows:
First, let's simplify the radicals separately:
√60 = √(6 * 10) = √6 * √10
2√5 = 2 * √5
Next, let's substitute these simplifications back into the expression:
(√6 * √10) / (2 * √5)
Now, let's simplify the expression further:
√10 / 2
Finally, we divide the numerator by the denominator:
√10 / 2 = (1/2) * √10
So, the simplified form of √60/2√5 is (1/2)√10.
To divide √60 by 2√5, we can follow these steps:
Step 1: Simplify the expression inside the square root.
√60 can be simplified by finding the perfect square that evenly divides 60. In this case, 4 is a perfect square that divides both 60 and 5.
√60 = √(4 * 15) = √4 * √15 = 2√15
Step 2: Substitute the simplified values back into the expression.
The expression now becomes:
(2√15) / (2√5)
Step 3: Cancel out the common factors.
In this case, both the numerator and denominator have a factor of 2. We can cancel it out.
(2√15) / (2√5) = (√15) / (√5)
Step 4: Rationalize the denominator.
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is √5 (the conjugate of √5 is also √5).
(√15) / (√5) * (√5) / (√5) = (√15 * √5) / (√5 * √5)
Step 5: Simplify the expression.
(√15 * √5) / (√5 * √5) = (√75) / 5
So, the simplified form of √60 / 2√5 is (√75) / 5.