GRE Math assist » Arithmetic » simple Squaring / Square roots » Square Roots and also Operations » how to divide square root

Which of the complying with is equal to 

*


*


*


*


*


Explanation:

*
 We then multiply our portion by 
*
 because we cannot leave a radical in the denominator. This provides us 
*
. Finally, we can simplify our fraction, splitting out a 3, leaving us with 
*


Explanation:

Let"s integrate the 2 radicals into one radical and also simplify.

You are watching: How to divide a square root

*
 

Remember, when splitting exponents of very same base, just subtract the power.

The final answer is 

*
.


Explanation:

If we multiplied top and also bottom by 

*
, us would acquire nowhere, as this would certainly result: 
*
. Instead, let"s cross-multiply.

*

*

*
 

Then, square both sides to remove the radical.

*

*
 

Divide both sides by 

*
.

*
 

The reason the an adverse is not response is due to the fact that a negative value in a radical is an imagine number.


Explanation:

We don"t desire to have radicals in the denominator. To eliminate radicals, just multiply top and also bottom by the radical.

*


Explanation:

There are two techniques we have the right to use to leveling this fraction:

Method 1:

Factor the numerator:

*
 

Remember, we need to variable out perfect squares.

 

Method 2: 

You can incorporate the portion into one big square root.

*
 

Then, you deserve to simplify the fraction.

*


Explanation:

Let"s element the square roots.

*
 

Then, main point the numerator and the denominator by 

*
 to get rid of the radical in the denominator.

*


Explanation:

We can definitely eliminate some answer choices. 

*
 and 
*
 don"t make sense since we have actually an irrational number. Next, let"s multiply the numerator and denominator of 
*
 by 
*
. When we leveling radical fractions, we shot to get rid of radicals, yet here, we room going to walk backwards.

*

*
, so 
*
 is the answer.


Explanation:

We don"t want to have radicals in the denominator. To eliminate radicals, simply multiply the numerator and the denominator by the radical.

*
*

Remember to distribute the radical in the numerator when multiplying.

This might be the answer; however, the numerator can be simplified. Let"s aspect out the squares. 

*
 

Finally, if we variable out a 

*
, we get:

*


Explanation:

Let"s eliminate the radicals in the denominator of every individual fraction.

*
 

Then uncover the least common denominator of the fractions, i beg your pardon is , and also multiply them so that they each have actually a denominator of .

*
 

We can absolutely simplify the numerator in the right portion by factoring out a perfect square of 

*
.

*

Finally, we can aspect out a 

*
:

*

That"s the last answer.


Explanation:

To eliminate the radical, we should multiply through the conjugate. The conjugate uses the the contrary sign and also multiplying by it will let us rationalize the denominator in this problem. The score is obtaining an expression of 

*
 in i m sorry we space taking the differences of 2 squares. 

*

This answer is the same as 

*
. Mental to distribute the negative sign.

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