Mathematics, 07.11.2019 04:31 jorgereyes01

Solving radical equations
how to solve radical equations

Solving radical equations how to solve radical equations

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Answer from: proxydayz

Simplify radical expressions. If we combine these two things then we get the product property of radicals and the quotient property of radicals. These two properties tell us that the square root of a product equals the product of the square roots of the factors. no radicals appear in the denominator of a fraction.

Answer from: drcarver

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.

Example 1

Solve equation.

Isolate the radical expression.

equation

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

equation

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

Applying the quadratic formula, equation

Now, check the results.

If equation, equation

If x = –5,

equation

The solution is equation or x = –5.

Example 2

Solve equation.

Isolate the radical expression.

equation

There is no solution, since equation cannot have a negative value.

Example 3

Solve equation.

Isolate one of the radical expressions.

equation

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

equation

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

equation

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

equation

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

Applying the quadratic formula, equation

Check the solutions.

If x = 10, equation

So x = 10 is not a solution.

If x = 2, equation

The only solution is x = 2.

Example 4

Solve equation.

Isolate the radical involving the variable.

equation

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.

equation

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

Answer from: Quest

she will sew have sewn five dresses and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

contact me if you have any questions you are welcome.