Radicals and Fractions
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Algebra II › Radicals and Fractions
Simplify, and ensure that no radicals remain in the denominator.
None of these
Explanation
Moving radical from the denominator to the numerator:
Factoring:
Simplifying:
Simplify the fraction:
Explanation
Multiply the numerator and denominator by the denominator.
Reduce the fraction.
The answer is:
Simplify:
Explanation
We can take the square roots of the numerator and denominator separately. Thus, we get:
Explanation
To simplify, first start by rewriting as:
.
Then, simplify the numerator and denominator separately.
and
.
Now, you have
.
Simplify to get
.
Rationalize the denominator.
Explanation
In order to rationalize the denominator, multiply both the numerator and denominator by square root five.
When a radical of a certain number is multiplied by itself, the radical will be eliminated, leaving only the integer.
This cannot be simplified any further.
The answer is:
Simplify:
Explanation
Simplify both the top and bottom of the fraction.
Cancel the common terms.
Rationalize the denominator by multiplying the top and bottom by root six.
Multiply the numerator with numerator and denominator with denominator.
Simplify the fraction.
The answer is:
Rationalize the denominator:
Explanation
In order to eliminate the radical sign, multiply the top and the bottom by the denominator.
Reduce the numerator and denominator.
The answer is:
Simplify, if possible:
Explanation
In order to eliminate the radical in the denominator, we will need to multiply the denominator twice on both the numerator and denominator.
Simplify the fraction.
Factor the inner term using common factors of numbers the power of three.
The answer is:
Rationalize the denominator:
Explanation
Multiply the top and bottom by the conjugate of the denominator.
Simplify the top and bottom of the fractions.
The answer is:
Evaluate:
Explanation
Multiply the denominator together to combine as one radical.
Rationalize the denominator by multiplying the top and bottom of the fraction by the denominator.
Reduce the fraction.
The answer is: