Question

Multiply. PLZ HLEP I AM CONFUSED 3√⋅2√2⋅58√⋅√18

Answer 1

Answer: 120√6

*I apologize for the late response, if any of you need this, I'm happy to help. If the explanation isn't clear, please message me and we can work from there. I have checked this answer 3 times and it has been correct all those three times.*

Question and procedure:

√3 x 2√2 x 5√8 x √18

To solve, first, you should simplify any roots that need simplifying.

The two roots that need simplifying are 5√8 and√18.

In 5√8, you can still simplify the √8, there are four factors of 8: 1,2,4,8. The only two factors that you will be able to further simplify are 2 and 4.

TO SOLVE:

√2 x √4 = 2√2

then, you multiply 2√2 x 5, getting you 10√2

( the root of 4 is 2)

THE OTHER ROOT:

√18: 18 has the following factors: 1,2,3,6,9,18. The two factors that you will be able to further simplify are 9 and 2.

So, √18 is 3√2.

Now we can solve the problem:

√3 x 2√2 x 10√2 x 3√2

( when solving, it is important to keep in mind that you are supposed to multiply the number OUTSIDE the root together and the numbers INSIDE of the root together)

√3 x 2√2 = 2√6.

2√6 x 10√2 = 20 √12

* WE ARE ABLE TO SIMPLIFY 20√12 into 40√3.

40√3 x 3√2 = 120√6.

Answer 2

Answer:

$\huge\boxed{120\sqrt6}$

Step-by-step explanation:

$\sqrt3\cdot2\sqrt2\cdot5\sqrt8\cdot\sqrt{18}\qquad\text{use}\ \sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\\\\=(2)(5)\sqrt{(3)(2)(8)(18)}\\\\=10\sqrt{(3)(2)(2)(2)(2)(2)(3)(3)}\\\\=10\sqrt{(3)(2)(2^2)(2^2)(3^2)}\\\\=10\sqrt{(2)(3)}\cdot\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=10\sqrt6\cdot2\cdot2\cdot3\\\\=10\sqrt6\cdot12\\\\=120\sqrt6$