what is the simplified form of 3 sqrt (5c) x sqrt (15c^3)
choices are
a. 15c^2 sqrt (3)
b.6c^2 sqrt (5)
c. 5c^2 sqrt(3)
d. 12c^4 sqrt(5)
please help i don't understand how to do the question
i would really appreciate it
3√(5c) (√(15c^3)
= 3√(75c^4)
= 3*√25*√3*c^2 , * implies multiplication
= 15√3 c^2 <==== better form than their choice a)
Why did the math book go to therapy?
Because it had too many square roots to deal with!
Now, let's tackle your question. To simplify the expression, we need to multiply the numbers outside the square roots and combine the variables inside the square roots.
Starting with the numbers, we have 3 multiplied by 15, which gives us 45. Now let's look at the variables. Inside the square root, we have "c" raised to powers. We have "c" to the power of 1 (5c) and "c" to the power of 3 (15c^3). When multiplying variables with the same base, you add the exponents. So we get c^(1+3) = c^4.
Putting it all together, the simplified expression is: 45c^4 sqrt(5).
But wait, that wasn't one of the answer choices! Don't worry, math problems can be tricky sometimes. Let's simplify it further.
The square root of 45 can be split into sqrt(9) and sqrt(5). The square root of 9 is 3, so we're left with 3sqrt(5)c^4sqrt(5).
Combining like terms, we get 3c^4sqrt(25) = 3c^4 * 5 = 15c^4.
So, the simplified form of 3 sqrt (5c) x sqrt (15c^3) is 15c^4.
If you're still confused, don't hesitate to ask for more help.
To simplify the expression 3sqrt(5c) x sqrt(15c^3), we can apply the product rule of square roots, which states that the product of two square roots is equal to the square root of their product.
Step 1: Multiply the coefficients and simplify any constants.
3 x 1 = 3
Step 2: Multiply the radicands, which are the values within the square roots.
5c x 15c^3 = 75c^4
Step 3: Combine the coefficients and the radicands.
3sqrt(5c) x sqrt(15c^3) = 3sqrt(75c^4)
Step 4: Simplify the square root of the product.
The square root of 75c^4 can be simplified as follows:
√(75c^4) = √(25 x 3 x c^2 x c^2) = (√25) x (√3) x (√c^2) x (√c^2) = 5c^2 √3
Therefore, the simplified form of 3sqrt(5c) x sqrt(15c^3) is 3(sqrt(75c^4)) = 3(5c^2 √3) = 15c^2 √3.
So, the answer is option c. 5c^2 sqrt(3).
To simplify the expression, you need to understand how to multiply radicals (square roots) and combine like terms. Let's break it down step by step.
The expression is: 3√(5c) * √(15c^3).
Step 1: Multiply the coefficients (numbers outside the radicals): 3 * 1 = 3.
The expression becomes: 3√(5c) * √(15c^3).
Step 2: Multiply the radicands (the numbers inside the radicals): 5c * 15c^3 = 75c^4.
The expression becomes: 3√(75c^4).
Step 3: Simplify the radical inside the expression. Since 75 can be factored into 3 * 5 * 5, and c^4 can be written as (c^2)^2, the expression becomes: 3 * √(3 * 5^2 * (c^2)^2) = 3 * √(3 * 5^2) * √((c^2)^2) = 3 * 5c^2 * √3 = 15c^2√3.
Therefore, the simplified form of 3√(5c) * √(15c^3) is option b. 6c^2√5.