So even this step that I did here, if you wanted, you could've Six times seven is 42 x times the square root of two x and the key thing to appreciate is I keep using this property that a radical of products or the square root of products is the same thing as a But what's valuable about this is we now see this is six times now we can take the the square root of 49 x squared this is going to seven x square root of 49 is seven square root of x squared is going to be x and then we multiply that times the square root of two x times the square root of two x and so now we're in the home stretch. Radical of the product of things, that's the same thing as the product of the radicals. What you have there, but, if you're taking the I could've put one big radical sign over 49 x squared times two x which would've been exactly The seven, the x squared I have a two x left. X squared 49 x squared and then I could once again separate the two The square root of let's put all the perfect squares first so seven times seven that is 49 that's those two. This is going to be six times and I could write it like this. So let's rewrite this a little bit to see what we can do. And then 14's not a perfect square, seven isn't a perfect square but seven times seven is. Especially because, from a variable point of view you can view this as a But when you're trying to factor out perfect squares, it's actually easier if it's in this factored form here. And we could've said, seven times 14 is what 98. And the reason why Iĭidn't multiply it out. Actually let me extend my radical sign a little bit. Seven times x and then let me actually factor 14. So six times the square root of and I'll actually I'll just leave it like this. And so this is going to be equal to six times and then the product of two radicals, you can view that as the This is going to be the same thing as two times three times the square root of seven x times the square root of 14 x squared. So, we can change the order of multiplication. Well, let's first just multiply this thing. Taking any perfect squares out multiplying and taking any perfect squares out of the radical sign. So let's say I have two times the square root of seven x times three times the square root of 14 x squared. FOIL or use extended distribution on the right side to eliminate the exponentsĩ) Check answer back in original equation to verify that it isn't an extraneous solution. The link above keeps them both on the same side.Ģ) Square both sides: ^2 = ^2ģ) Simplify left side. I'll get you started on your equation: √(x+15) + √(x) = 15ġ) I would move one radical to the other side. You have a radical equation, not a radical expression.įor a problem more like yours, I would suggest you look at the 2nd problem at this link: First, you are in the wrong section of lessons.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |