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damaskus [11]
2 years ago
5

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

Mathematics
2 answers:
photoshop1234 [79]2 years ago
7 0

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).

grandymaker [24]2 years ago
6 0

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

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