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solving problems involving radical equations

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Radical Expressions and Equations

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Quadratic Equations and Functions

Rational Expressions and Functions

solving problems involving radical equations

Alissa Fong

MA, Stanford University Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

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Solving Radical Equations - Problem 3

This problem is kind of crazy-looking because not only is it 2 equal fractions, but it also involves square roots. For me whenever I see two equal fractions or a proportion, I like to use cross multiplying. Cross multiplying is where you write an equality statement as the product of the two diagonals. So I’ll have root 2 times 5 root 2, that’s these diagonals is going to be equal to the product of x times root 2 take away 1. Just be really careful with your parentheses, make sure x is being multiplied by both of those terms. Okay well let’s go through and solve that. Root 2 time 5 root 2 is going to be 5 times 2 which is 10. 10 is equal to x times root 2 take away 1. Now usually I want to distribute something like this, but since x is being multiplied by some number like the square root of 2 take away 1 is like .4 or something, it’s some number and I’m going to want to get x all by itself. I’m not going to distribute. What I’m going to do at this step is divide both sides by the quantity root 2 take away 1 because now x is isolated. I know that x is equal to 10 over root 2 take away 1 and that’s kind of my answer, except that this is not proper form. You guys know thou shall not have a radical on the denominator of a fraction, it’s just not simplified form. So the way I would simplify that answer is by multiplying by the Conjugate of the denominator. I’m going to multiply top and bottom by root 2 plus 1. The reason why that works is because when I FOIL on the bottom here, I’ll have just an integer on my denominator. Here is what I mean. Root 2 times root 2 is regular old 2, that’s my firsts, outers I’ll have minus root 2, inners is plus root 2 so those guys are added inverses they become 0 at the end I need -1. On top of my fraction if I distribute the 10 I’ll have 10 root 2 plus 10. I’m almost done. The last thing I want to do is simplify that denominator there. This will be my final answer, 10 root 2 plus 10 divided by 1 which means I don’t have to write it. 10 root 2 plus 10 equals x, that’s my final answer. Your textbook might have in the back of the book this 10 factored out, so it might say 10 parenthesis root 2 plus 1, it doesn’t matter those are equivalent statements. So again guys cross multiplying is a great technique you learned months and months ago, but you can still use it to solve these problems. Be really careful when you get to something where x equals blah, blah, blah, make sure that blah, blah, blah is in reduced form. This guy needs to be multiplied by the conjugate in order to be simplified. I have to get that radical out of the denominator.

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solving problems involving radical equations

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solving problems involving radical equations

A radical equation is an equation in which a variable is under a radical. To solve a radical equation:

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.

solving problems involving radical equations

Isolate the radical expression.

solving problems involving radical equations

Raise both sides to the index of the radical; in this case, square both sides.

solving problems involving radical equations

This quadratic equation now can be solved either by factoring or by applying the quadratic formula.

solving problems involving radical equations

Now, check the results.

solving problems involving radical equations

Isolate one of the radical expressions.

solving problems involving radical equations

This is still a radical equation. Isolate the radical expression.

solving problems involving radical equations

This can be solved either by factoring or by applying the quadratic formula.

solving problems involving radical equations

Check the solutions.

solving problems involving radical equations

So x = 10 is not a solution.

solving problems involving radical equations

The only solution is x = 2.

solving problems involving radical equations

Isolate the radical involving the variable.

solving problems involving radical equations

Since radicals with odd indexes can have negative answers, this problem does have solutions. Raise both sides of the equation to the index of the radical; in this case, cube both sides.

solving problems involving radical equations

The check of the solution x = –15 is left to you.

Previous Quiz: Solving Equations in Quadratic Form

Next Quiz: Solving Radical Equations

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IMAGES

  1. Solving Radical Equations

    solving problems involving radical equations

  2. Applications Using Radicals

    solving problems involving radical equations

  3. Radical Equations

    solving problems involving radical equations

  4. Solving Radical Equations

    solving problems involving radical equations

  5. Solving Radical Equations

    solving problems involving radical equations

  6. Solving Problems Involving Radical Expressions

    solving problems involving radical equations

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COMMENTS

  1. Radical Equation Calculator

    Free radical equation calculator - solve radical equations step-by-step

  2. Solving Problems Involving Radical Equations

    Solving Problems Involving Radical Equations - Free download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online for free. enjoy math

  3. Solving Radical Equations

    Time-saving video that explains how to solve any equation with radicals (square roots). Example problems have roots of variable expressions and trinomials, and use cross products

  4. Solving Radical Equations

    A radical equation is an equation in which a variable is under a radical

  5. Solve Equations Involving Radicals

    To solve an equation involving radicals, inverse operations are used to solve for the variable. A radical involving the square root of a number can be evaluated by determining the square root of the number under the radical sign