Question

Find the simplified product sqrt 2x^3 sqrt 18x^5

Answer 1

The first step to solving this is to remember the radical rules. They state that the product of roots that have the same index are equal to the root of the product. Knowing this,, the expression changes to the following:
$\sqrt{2 x^{3} X 18 x^{5} }$
Next you'll add the two exponents together and then calculate the product.
$\sqrt{36 x^{8} }$
Lastly,, calculate the square root to find your answer.
6$x^{4}$
This means that the correct answer to your question will be 6$x^{4}$.
Let me know if you have any further questions
:)

Answer 2

Hello there!

$\sqrt{2x ^{3} } \sqrt{18x ^{5} }$

We need to use the Radical Rules.

Do you know it?

Answer; The product of roots with the same index is equal to the root of the product.

What does that even mean? Well, it means that we need to multiply all of them under the same square root.

$\sqrt{2x ^{3} * 18x ^{5} }$

Ok so now we need to calculate the product.

To calculate the product, we need to multiply the base together and we need to add the exponent together.

2 * 18 = 36 and 3 + 5 which are the exponents = 8

So, it looks like that:

$\sqrt{36 x^{8} }$

Here we go again! Now we need to calculate the square root. (We are almost there!)

The root of a product is equal to the product of the roots of each factor.

So it looks like this:

$\sqrt{36} \sqrt{x^8}$

Now we need to write it in exponential form:

$\sqrt{6^2} x^4$

When we reduce the index of the radical and the exponent with 2, we find the final answer, which is:

Answer: $6x^4$


Let me know if you have any questions about the answer. As always, it is my pleasure to help students like you!