Divide √60.
—
2√5
To divide √60 by 2√5, we can simplify the expression by rationalizing the denominator.
First, let's express √60 and 2√5 in their simplified forms:
√60 = √(4 * 15) = 2√15
2√5 remains the same.
Now, the expression becomes:
(2√15) / (2√5)
Since the denominators are the same, we can divide the numerators:
2√15 / 2 = √15
Therefore, √60 / (2√5) simplifies to √15.
To divide √60 by 2√5, we can use the rationalizing technique to simplify the expression.
Step 1: Rationalize the denominator of 2√5.
Multiply the numerator and denominator by the conjugate of 2√5, which is also 2√5.
(√60)/(2√5) * (√5)/(√5) = (√300)/10
Step 2: Simplify the numerator.
√300 can be further simplified as √(100 * 3) = √(10^2 * 3) = 10√3
So the expression becomes:
(10√3)/10
Step 3: Cancel out the common factor of 10.
Dividing 10√3 by 10 results in:
√3
Therefore, √60 divided by 2√5 simplifies to √3.
To divide the expression √60 by 2√5, you need to simplify it using the rules of rationalizing the denominator.
Step 1: Simplify the expression
√60 can be simplified as follows:
√60 = √(2^2 * 3 * 5) = 2√15
Step 2: Rewrite the division expression
The division expression √60 / 2√5 can be written as:
(2√15) / (2√5)
Step 3: Rationalize the denominator
To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator, which is 2√5:
[(2√15) / (2√5)] * [(2√5) / (2√5)]
= (2√15 * 2√5) / (2√5 * 2√5)
= (4√75) / (20)
Step 4: Simplify the expression
To simplify further, we can simplify the square root of 75 as follows:
√75 = √(5^2 * 3) = 5√3
Substituting this back into our expression, we have:
(4√75) / (20) = (4 * 5√3) / (20)
Step 5: Simplify the fraction
We can simplify the fraction by canceling out common factors:
(4 * 5√3) / (20) = (4 * √3) / (4)
= √3
Therefore, √60 / 2√5 simplifies to √3.