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

Answer:

$18\sqrt2$

Step-by-step explanation:

To simplify:

$2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }$

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

$18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}$

The pairs are underlined as above.

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

Now, taking square roots.

$\sqrt{18} =3 \sqrt2$

$162 = 3 \times 3 \times \sqrt 2 = 9 \sqrt2$

So, the given expression becomes:

$2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}$

So, the answer is:

$18\sqrt2$ or 18 StartRoot 2 EndRoot