WEBVTT
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Welcome to Brainfuse!
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We are about to solve radical equations
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To do that
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We have our sample problem
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It asks which problem below is a radical equation? Identify that problem
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And solve for x.
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Okay, so what is a radical equation? Well, I see radicals in both of these equations
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So which one is a radical equation?
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Well they both have radicals
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But to be a radical equation, the problem needs
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A radical with a variable in it
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Okay, so these two have constants in it so it doesn't pass the test.
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This one is
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Our radical equation because we have the square root of x plus 6 in the equation
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Otherwise known as
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Radical x + 6.
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So now
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Because we have identified it we need to solve it.
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There's always a catch.
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First we want to
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See if we can isolate the radical because that will make our lives
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Much much easier.
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Okay so I want the radical x plus 6 on one side
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And we're going to move that 8 to the other side
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By adding 8 to both sides, so it equals zero on the left
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And 8 on the right.
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If working with square roots, make sure that the answer is positive,
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Because remember a square root cannot
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Be equal to a negative number
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Okay
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Now that we've isolated the radical we can square both sides
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And I'm emphasizing both
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Sides of the equation
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Not each term
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And we'll see in the next problem why that's important. Okay so radical x plus 6 squared is x + 6,
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Equals 8 squared, that's 64.
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Now we just solve for x and life is good
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So x equals
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58.
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Any time you have a radical equation be sure to check the answer, because squaring numbers,
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Especially more than once, can lead you to some false results
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So to check it we have
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58 + 6
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Minus 8 equals
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0. Okay, 58 + 6 is 64
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Minus 8 equals 0 and yes, square root
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Of 64 is 8, so
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Cha-ching!
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That is correct.
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So our final step was to check the solution
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And this is especially important with radical equations
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When you square both sides, extraneous roots may be introduced so you need to check to see if the
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Original equation is satisfied by your answers. You do this by plugging in each answer
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To the left side then the right side of the equation. If that answer makes the sides equal
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Then it's correct.
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Now it's your turn to solve some radical equations
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And make sure to check your answers. Thanks.