what is the simplified form of
3sq rt 5c * sq rt 15c^3?
A.15c^2 sq rt 3
B.6c^2 sq rt 5
c.5c^2 sq rt 3
d.12c^4sq rt 5
I think it is A...?
A is correct answer
To simplify the expression 3√(5c) * √(15c^3), we can combine the factors inside the square roots.
First, let's simplify the square root of 5c: √(5c) = √5 * √c = √5c.
Next, let's simplify the square root of 15c^3: √(15c^3) = √(3 * 5 * c^2 * c) = c√(3 * 5 * c) = c√(15c).
Now, we can rewrite the entire expression as: 3√(5c) * √(15c^3) = 3(√5c)(c√(15c)).
Multiplying the terms together, we get: 3(√5c)(c√(15c)) = 3c√(5c) * c√(15c) = 3c * c * √(5c * 15c) = 3c^2√(75c^2) = 3c^2√(25 * 3c^2) = 3c^2 * 5c√3 = 15c^2√3.
Therefore, the simplified form is 15c^2√3. So, the correct answer is C.
To simplify the expression 3√5c * √15c^3, we follow these steps:
Step 1: Combine the coefficients (numbers in front of the square root) by multiplication. In this case, 3 * 1 = 3.
Step 2: Multiply the variables (letters) by adding their exponents. In this case, c^1 * c^3 = c^(1+3) = c^4.
Step 3: Multiply the square roots of the numbers inside the root symbol (√5 * √15). Simplify the product if possible.
- √5 is already simplified because there are no perfect square factors inside the root.
- √15 can be simplified because it has a perfect square factor of 3 (3 * 5). Rewrite it as √3 * √5.
Step 4: Combine the simplified square roots (√5 * √3) by multiplication. The result is √(5 * 3) = √15.
Putting everything together, we have 3√5c * √15c^3 = 3c^4√15.
Therefore, the simplified form of the expression is 3c^4√15, which corresponds to option D. So, your initial assumption was incorrect. The correct answer is d. 12c^4√5.