Which of the following is equal to
Let"s combine the two radicals into one radical and simplify.
You are watching: How to divide a square root
Remember, when dividing exponents of same base, just subtract the power.
The final answer is
If we multiplied top and bottom by
Then, square both sides to get rid of the radical.
Divide both sides by
The reason the negative is not an answer is because a negative value in a radical is an imaginary number.
We don"t want to have radicals in the denominator. To get rid of radicals, just multiply top and bottom by that radical.
There are two methods we can use to simplify this fraction:
Factor the numerator:
Remember, we need to factor out perfect squares.
You can combine the fraction into one big square root.
Then, you can simplify the fraction.
Let"s factor the square roots.
Then, multiply the numerator and the denominator by
We can definitely eliminate some answer choices.
We don"t want to have radicals in the denominator. To get rid of radicals, just multiply the numerator and the denominator by that radical.
Remember to distribute the radical in the numerator when multiplying.
This may be the answer; however, the numerator can be simplified. Let"s factor out the squares.
Finally, if we factor out a
Let"s get rid of the radicals in the denominator of each individual fraction.
Then find the least common denominator of the fractions, which is , and multiply them so that they each have a denominator of .
We can definitely simplify the numerator in the right fraction by factoring out a perfect square of
Finally, we can factor out a
That"s the final answer.
To get rid of the radical, we need to multiply by the conjugate. The conjugate uses the opposite sign and multiplying by it will let us rationalize the denominator in this problem. The goal is getting an expression of
This answer is the same as
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