Question

What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot 6 StartRoot 2 EndRoot 18 StartRoot 2 EndRoot 30 StartRoot 2 EndRoot 36 StartRoot 2 EndRoot

Answer 1

its B. 18 sqrt(2)

Explanation:

just took test

Answer 2

`18\sqrt2`

Explanation:

To simplify:

`2 √(18)+ 3 \sqrt2+ √(162 )`

First of all, let us write 18 and 162 as product of prime factors:

`18 = 2 * \underline{3 * 3}\\162 = 2 * \underline{3 * 3} * \underline{3 * 3}`

The pairs are underlined as above.

While taking roots, only one of the numbers from the pairs will be chosen.

Now, taking square roots.

`√(18) =3 \sqrt2`

`162 = 3 * 3 * \sqrt 2 = 9 \sqrt2`

So, the given expression becomes:

`2 √(18)+ 3 \sqrt2+ √(162 ) = 2 * 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}`

So, the answer is:

`18\sqrt2` or 18 StartRoot 2 EndRoot