Question

What is the simplified form of the following expression?

Answer 1

$2 \sqrt{18} +3 \sqrt{2} + \sqrt{168} =25.558$
A. 8.485
B. 25.558
C. 42.426
D. 50.911

B. $18 \sqrt{2}$ is your answer

Answer 2

Answer:

Option B is correct.

The simplified form of the given expression is, $18\sqrt{2}$.

Explanation:

Given the expression:  $2\sqrt{18} +3 \sqrt{2} +\sqrt{162}$

Square root of a number is a value that when multiplied by itself, gives the number.

$\sqrt{a^2}=\sqrt{a \times a}$= a

we can write the given expression as;

$2\sqrt{9 \times 2} +3\sqrt{2} +\sqrt{2 \times 81}$ or

$2\sqrt{3^2 \times 2}+3 \sqrt{2} +\sqrt{9^2 \times 2}$

Then by definition of square root,

$2 \cdot 3 \sqrt{2} +3\sqrt{2}+9 \sqrt{2}$ or

$6\sqrt{2} +3\sqrt{2} +9\sqrt{2} = 18\sqrt{2}$

Therefore, the simplified form of the given expression is, $18\sqrt{2}$ .