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)