Question
Divide (sqrt(60))/(2sqrt(5))
Answers
GPT 3.5
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.
√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.