Question

simplify the radical expression
-3*(squareroot)180h^4

Answer 1

Is this the equation?\[-3\sqrt{180h ^{4}}\]

Answer 2

yes lol

Answer 3

First, when you have two terms multiplying each other under a square root you can separate them so they are just two square roots multiplying each other, like this:\[-3\sqrt{180}\sqrt{h ^{4}}\]
Then look at the sqrt{180}... you can split that up into factors. What times what equals 180? Lots of things, but look for numbers that will simplify your equation. For example, 5 times 36 gives 180, and 36 is something that will simplify things:\[-3\sqrt{5}\sqrt{36}\sqrt{h ^{4}}\] Then, well the square root of 36 is just 6. So\[-3*6*\sqrt{5}\sqrt{h ^{4}}\] Next look at the last term, the square root of h to the power of 4. Well, a square root simply means that you're taking something to the power of 1/2 so you can rewrite that square root as:\[\sqrt{h ^{4}}=(h ^{4})^{1/2}\] Multiply those exponents 4 times 1/2 is 2. So you just have\[\sqrt{h ^{4}}=h ^{2}\]
So your final equation is:\[-18h ^{2}\sqrt{5}\]