Simplify the given square root. − 75 \sqrt{-75} − 75 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

Hey, y'all. Let's take a look at this practice problem. So I wanna simplify this square root, and I have the square root of negative 75. Now whenever I have the square of a negative number, I can always simplify this into I times the square root of whatever my number is and then simplify it from there. So I have my I pulled out and I can go ahead and simplify or expand the 75 into 25 times 3. So further simplifying this, 25 is a perfect square, so I can go ahead and pull that out as a 5 and I'm left with I times 5 and then that 3 has to say in my radical. Now whenever we get answers like this, we always wanna pull our whole number in front of our imaginary unit. So here we're gonna end up with 5 I root 3 and that is our solution. That's all for this one. I'll see you in the next one.

Simplify the given square root. −75\sqrt{-75}−75

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Simplify the given square root. $\sqrt{-75}$