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

2 Answers

3 votes

Answer:

18√2

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

User Funk Soul Ninja
by
6.8k points
3 votes

Answer:

Simplified form is
√(2)( 18).

Explanation:

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

To find : What is the simplified form.

Solution : We have given
2√(18) + 3√(2) +√(162).

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


2√(9 * 2) + 3√(2) +√(81 * 2).

By radical rule :
√(a * b) = √(a) * √(b)


2 * 3√( 2) + 3√(2) +9\ √(2).


6√( 2) + 3√(2) +9\ √(2).

Taking common
√(2) from each term


√(2)( 6 +3 + 9).


√(2)( 18).

Therefore, Simplified form is
√(2)( 18).

User Federico Squartini
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6.4k points