Question

What is the simplified form of the following expression? 2 Sqrt 18+3 Sqrt 2 + Sqrt 162

Answer 1

Answer:

Simplified form is $\sqrt{2}( 18)$.

Step-by-step explanation:

Given :  2 Sqrt 18+3 Sqrt 2 + Sqrt 162.

To find : What is the simplified form.

Solution : We have given  $2\sqrt{18} + 3\sqrt{2} +\sqrt{162}$.

We can write 18 as 9 *2 and 162 as 81 *2.

$2\sqrt{9 * 2} + 3\sqrt{2} +\sqrt{81 * 2}$.

By radical rule : $\sqrt{a * b} = \sqrt{a} * \sqrt{b}$

$2 * 3\sqrt{ 2} + 3\sqrt{2} +9\ \sqrt{2}$.

$6\sqrt{ 2} + 3\sqrt{2} +9\ \sqrt{2}$.

Taking common $\sqrt{2}$ from each term

$\sqrt{2}( 6 +3 + 9)$.

$\sqrt{2}( 18)$.

Therefore, Simplified form is $\sqrt{2}( 18)$.

Answer 2

Answer:

18√2

Step-by-step explanation:

2√18 + 3√2 + √162

= 2√(9 * 2) + 3√2 + √(81 * 2)

= (2 * 3)√2 + 3√2 + 9√2

= 6√2 + 3√2 + 9√2

= (6 + 3 + 9)√2

= 18√2