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

sqrt(2)xx(-3)sqrt(3)

3 Answers
Jun 19, 2018

Around... -7.14

Explanation:

First, we need to simplify the square roots.

sqrt2=1.414...

sqrt3=1.732...

1.7xx-3=-5.1

So now you have the two answers you need to xx them.

1.4xx-5.1=-7.14

Hope this helped.

Jun 19, 2018

-3sqrt(6)

Explanation:

Note that positive xx negative gives negative. So our answer will be negative.

Now lets look at the numbers

Write as: -3xxsqrt(2)xxsqrt(3) color(white)("d")->color(white)("d") -3sqrt(2)sqrt(3)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lets try an idea out using numbers we know

2xx5=10

sqrt(2^2)xxsqrt(5^2) ->sqrt(4)sqrt(25) ->color(red)(sqrt(4xx25))->sqrt(100) = 10

So sqrt(a)xxsqrt(b) = sqrt(axxb)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using the above logic:

-3sqrt(2)sqrt(3) ->-3sqrt(2xx3) =-3sqrt(6)

The numbers in under roots will be multiplied together

Explanation:

In general, a^nb^n=(ab)^n

\sqrt2\cdot(-3\sqrt3)=-3\sqrt2\sqrt3-3\sqrt{2\cdot 3}=-3\sqrt6