Divide (sqrt(60))/(2sqrt(5))
To simplify the expression, we can combine the square roots with the same bases.
√60 can be simplified to 2√15 since 15 is the largest perfect square that divides 60.
So, the expression becomes: (2√15) / (2√5).
Now, we can cancel out the common factor of 2:
(2√15)/(2√5) = (√15)/√5.
To simplify further, we multiply the numerator and denominator by the conjugate of the denominator (√5).
(√15)/√5 x (√5)/(√5) = (√(15*5))/(√(5*5)) = √75/√25.
√75 can be simplified to 5√3 since 3 is the largest perfect square that divides 75,
and √25 simplifies to 5.
So, the final simplified expression is:
5√3/5 = √3.
Therefore, (sqrt(60))/(2sqrt(5)) simplifies to √3.
To divide the expression (sqrt(60))/(2sqrt(5)), we can simplify it by rationalizing the denominator.
Step 1: Simplify the numerator and denominator individually.
- The square root of 60 can be simplified as follows:
sqrt(60) = sqrt(2^2 * 2 * 3 * 5) = 2sqrt(15)
- The square root of 5 remains the same.
Step 2: Rewrite the expression with simplified terms.
Now our expression becomes:
(2sqrt(15))/(2sqrt(5))
Step 3: Apply the division of fractions.
When dividing by a fraction, you can multiply by its reciprocal. In this case, we have:
(2sqrt(15))/(2sqrt(5)) * (1/(2sqrt(5)))
Step 4: Simplify further.
- The 2 in the numerator cancels out with the 2 in the denominator, leaving us with:
sqrt(15)/(sqrt(5))
- Rationalize the denominator:
To rationalize the denominator, multiply both the numerator and the denominator by sqrt(5):
[ sqrt(15) * sqrt(5) ] / [ sqrt(5) * sqrt(5) ]
Simplifying this further:
(sqrt(15) * sqrt(5)) / 5
And finally, we have:
sqrt(75) / 5
Therefore, the simplified result of (sqrt(60))/(2sqrt(5)) is sqrt(75) / 5.
To divide the expression (sqrt(60))/(2sqrt(5)), you can simplify it by rationalizing the denominator.
Step 1: Simplify the square roots.
√60 can be simplified as follows: √(6 * 10) = √6 * √10. Therefore, the expression becomes (√6 * √10) / (2√5).
Step 2: Rationalize the denominator.
To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of 2√5 is 2√5. So, multiply both the numerator and denominator by 2√5.
(√6 * √10 * 2√5) / (2√5 * 2√5)
Step 3: Simplify.
The denominator simplifies to 2 * 5 = 10.
The numerator simplifies to √6 * √10 * 2 = 2√60.
The expression now becomes 2√60 / 10.
Step 4: Further Simplify.
Divide both the numerator and denominator by 2.
Final expression: √60 / 5
Therefore, the simplified form of (sqrt(60))/(2sqrt(5)) is √60 / 5.