can someone correct these for me plz....
Problem#36
Use Property 2 to simplify each of the following radical expressions.
Radical (10)/(49)
My answer: (radical(2 times 5))/(7)
Use the properties for radicals to simplify each of the following expressions. Assume that all variables represent positive real numbers.
Problem #42
radical (5)/(3)
My answer: (radical(15))/(3)
Problem #48
(Radical (12x^3))/(5)
My answer: (2)/(5)x radical(15x)
correct, if I follow your notation.
To verify if your simplifications are correct, let's go through each problem step-by-step:
Problem #36:
You were asked to simplify the radical expression (√10)/49 using Property 2. Property 2 states that √(a/b) = (√a)/(√b).
So, applying Property 2 to the given expression, we have:
(√10)/49 = (√10)/(√49)
Now, let's simplify the denominator √49 = 7 since the square root of 49 is 7. Therefore:
(√10)/(√49) = (√10)/7
Your answer, (√(2*5))/7, is correct.
Problem #42:
You were asked to simplify the radical expression √5/3. To simplify, it's important to note that the square root only applies to the numerator (5) and not the denominator (3).
Therefore, √5/3 cannot be simplified further. Your answer, (√15)/3, is incorrect.
Problem #48:
You were asked to simplify the radical expression (√(12x^3))/5. To proceed, let's break down the expression into its factors:
(√(12*x*x*x))/5
Next, we extract perfect square factors from under the square root:
(√(4*3*x*x*x))/5 = (√4*√3*√x*√x*√x)/5
Simplifying further:
(2*x*√3)/5 * x√3
Now, rewriting the expression in a simplified form:
(2 * x * x * √3) / 5 = (2x^2 * √3) / 5
Therefore, your answer, (2/5)x√(15x), is correct.
To summarize:
Problem #36: (√10)/49 = (√(2*5))/7 = (√2)/7 * (√5)/7 (or √2/7√5 if the denominator is kept rational)
Problem #42: √5/3 cannot be simplified further.
Problem #48: (√(12x^3))/5 = (2 * x * x * √3) / 5 = (2/5)x√(15x)