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NikAS [45]
3 years ago
14

Solving radical equations How to solve radical equations

Mathematics
2 answers:
Dafna1 [17]3 years ago
8 0
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.
lozanna [386]3 years ago
5 0

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.

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0.136363636 as a fraction
Alex787 [66]

Answer:

0.136363636 = 34090909 / 250000000

Step-by-step explanation:

8 0
2 years ago
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What is the quotient in simplified form? State any restrictions on the variable. Show Work.
photoshop1234 [79]
    a+2           a +1
= -------  / ------------------
    a -5      (a - 3)(a - 5)

    a+2           (a - 3)(a - 5)
= -------  *  ------------------
    a -5              a +1

    (a+2)(a - 3)
= ----------------
        a +1

a NOT equal 5 and -1
5 0
3 years ago
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The diameter of a circle is 4 kilometers. What is the circle's circumference?
scZoUnD [109]

Answer:

12.57 km

Step-by-step explanation:

Radius = 4 / 2 = 2 km

Circumference = 2πr = 2π(2) = 4π = 12.57 km

6 0
2 years ago
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Using the image above, if the density of the LEGO piece is 0.85 g/cm^3, what COULD be a possible measurement for the density of
grin007 [14]

The Lego is submerged under the oil and therefore, is more dense than the oil

The possible density of the oil is the option;

<u>0.79 g/cm³</u>

Reason:

Given:

The density of Lego = 0.85 g/cm³

Density of oil = Required

Solution:

The density of an object is the mass per unit volume it occupies

  • Density = \dfrac{Mass}{Volume}

Increase in density increases the mass a unit volume occupies, therefore, a

more dense object is heavier than a less dense object such that the less

dense object will float on a dense object

The oil is floating on the Lego, therefore, the Lego is more dense than the

oil, and we have;

  • Density of Lego > Density of oil

The density of Lego = 0.85 g/cm³

Therefore;

0.85 g/cm³ > Density of oil

From the given options, the option that has a density less than 0.85 g/cm³ is the the option 0.79 g/cm³

Therefore, the possible density of the oil is <u>0.79 g/cm³</u>

<u />

Learn more here:

brainly.com/question/12864420

6 0
2 years ago
Please need help with this question m
katovenus [111]

Answer:

D.

Step-by-step explanation:

3(5)+2 > 14= 17>14 which is true

10-5 less than or equal to 7

true, 5 is less than 7

7 0
3 years ago
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