Question

What is the simplified form of the following expression? 2 startroot 18 endroot 3 startroot 2 endroot startroot 162 endroot

Answer 1

The simplified form of the provided expression of 2 startroot 18 endroot +3 startroot 2 endroot startroot +162 endroot is 18√2.

What is the simplified form of an equation?

The simplified form of an equation is the simplest way of expressing the equation, by applying the required operations of mathematics.

The equation provided in the problem is,

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

Let the simplified form of the above expression is n. Thus,

$n=2\sqrt{18}+3\sqrt{2}+\sqrt{162}$

Rewrite the equation to solve it further as,

$n=2\sqrt{3\times3\times2}+3\sqrt{2}+\sqrt{9\times9\times2}\\n=2\sqrt{3^2\times2}+3\sqrt{2}+\sqrt{9^2\times2}$

The square of the term cancel out the square root of it. Thus,

$n=2\times3\sqrt{2}+3\sqrt{2}+9\sqrt{2}\\n=6\sqrt{2}+3\sqrt{2}+9\sqrt{2}\\n=(6+3+9)\sqrt{2}\\n=18\sqrt{2}$

Thus, the simplified form of the provided expression of 2 startroot 18 endroot +3 startroot 2 endroot startroot +162 endroot is 18√2.

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