Radicals - Algebra 2

To solve, perform inverse opperations, keeping in mind order of opperations:

first, square both sides

subtract 1

divide by 2

To solve, perform inverse opperations, keeping in mind order of opperations:

take the square root of both sides

subtract 19 from both sides

square both sides

In order to add the two terms, we must first find the values of each term in the expression.

Rewrite the fractional exponents as an expression of a square root.

Add the two values.

The answer is:

Fractional exponents have the power as the numerator and the root as the denominator.

Fractional exponents have the power as the numerator and the root as the denominator.

In this case, the power is 5, and the root is 3.

The numbers with the fractional exponents can be rewritten as radicals.

Simplify both radicals. The sixth root of 64 is two.

The answer is:

This can be rewritten as the fourth root.

Rewrite the inner quantity with factors of numbers to the fourth root.

Simplify both terms.

The answer is:

To solve, use inverse opperations keeping in mind order of opperations:

divide both sides by 5

square both sides

add 12 to both sides

When working with radicals, a helpful step is to square both sides of an equation so that you can remove the radical sign and deal with a more classic linear or quadratic equation. But of course if you were to simply square both sides first here, you would still end up with radical signs, as were you to FOIL the left side you wouldn't eliminate the radicals. So a good first step is to add and subtract from both sides so that you get:

Now when you square both sides, you'll eliminate the radical on the right-hand side and yield:

Then when you subtract from both sides to set up a quadratic equalling zero, you have a factorable quadratic:

This factors to:

Which would seem to yield solutions of and . However, when you're solving for quadratics it's always important to plug your solutions back into the original equation to check for extraneous solutions. Here if you plug in the math holds: because , and .

But if you plug in , you'll see that the original equation is not satisfied: because does not equal . Therefore the only proper answer is .

To solve, first square both sides:

squaring the left side just givs x - 3. To square the left side, use the distributite property and multiply :

This is a quadratic, we just need to combine like terms and get it equal to 0

now we can solve using the quadratic formula:

This gives us 2 potential answers:

and

To get rid of the radical, we square both sides.

To get rid of the radical, we need to square both sides. The issue is radicals don't generate negative numbers unless we talk about imaginary numbers. In this case, our answer choice should be no answer.

Square both sides to get rid of the radical.

Subtract on both sides.

Subtract two from both sides.

Simplify the equation.

Square both sides.

Add on both sides.

Subtract on both sides.

The answer is:

Square both sides to get rid of the radical.

Add on both sides.

Square both sides to get rid of the radical.

Divide on both sides.

Square both sides to get rid of the radical.

Multiply on both sides.

In order to rewrite a radical as an exponent, the number in the radical that indicates the root, gets written as a fractional exponent as shown below:

In this case, we are done because there are no further simplification steps.

In order to solve this expression, we will need to rewrite each square root using one half as the exponent. This will allow us to solve for the value of the inner terms.

We can then rewrite the radical using factors of perfect numbers raised to the fourth power, such as:

The answer is: