# How do you multiply \sqrt { 2} \cdot - 3\sqrt { 3}?

## $\sqrt{2} \times \left(- 3\right) \sqrt{3}$

Jun 19, 2018

Around... $- 7.14$

#### Explanation:

First, we need to simplify the square roots.

$\sqrt{2} = 1.414 \ldots$

$\sqrt{3} = 1.732 \ldots$

$1.7 \times - 3 = - 5.1$

So now you have the two answers you need to $\times$ them.

$1.4 \times - 5.1 = - 7.14$

Hope this helped.

Jun 19, 2018

$- 3 \sqrt{6}$

#### Explanation:

Note that positive $\times$ negative gives negative. So our answer will be negative.

Now lets look at the numbers

Write as: $- 3 \times \sqrt{2} \times \sqrt{3} \textcolor{w h i t e}{\text{d")->color(white)("d}} - 3 \sqrt{2} \sqrt{3}$

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Lets try an idea out using numbers we know

$2 \times 5 = 10$

$\sqrt{{2}^{2}} \times \sqrt{{5}^{2}} \to \sqrt{4} \sqrt{25} \to \textcolor{red}{\sqrt{4 \times 25}} \to \sqrt{100} = 10$

So $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$
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Using the above logic:

$- 3 \sqrt{2} \sqrt{3} \to - 3 \sqrt{2 \times 3} = - 3 \sqrt{6}$

The numbers in under roots will be multiplied together

#### Explanation:

In general, ${a}^{n} {b}^{n} = {\left(a b\right)}^{n}$

$\setminus \sqrt{2} \setminus \cdot \left(- 3 \setminus \sqrt{3}\right) = - 3 \setminus \sqrt{2} \setminus \sqrt{3} - 3 \setminus \sqrt{2 \setminus \cdot 3} = - 3 \setminus \sqrt{6}$