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

Question

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

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Answer 1 · 2018-06-19T15:33:34

Around... #-7.14#

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.

Answer 2 · 2018-06-19T15:34:58

#-3sqrt(6)#

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) #

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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)#
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Using the above logic:

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

Answer 3 · 2018-06-19T15:35:29

The numbers in under roots will be multiplied together

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

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