You can put this solution on YOUR website! and
With negative radicands (expressions inside a radical are called radicands) both of these square roots represent imaginary numbers. So not only will we simplify the square roots we will also be expressing them in terms of "i" (which is defined to be equal to ).
We will factor -1's and perfect squares in each radicand: and
Next we use a property of radicals, , to split up the square roots of the products into products of the square roots of the factors: and
The square roots of -1 turn into i's and the square roots of the perfect squares simplify: and
We can rearrange the factors in each expression, using the Commutative Property. Some people prefer this form: and
with the square root at the end. By having the square root at the end there is no possible confusion about what is inside and what is not inside the square root.
Other prefer the form: and
because variables/letters usually go at the back. But this form, especially when hand-written, can be confusing as to whether the i is inside or outside the square root.
Personally I prefer the first form most of the time.
If the "and" meant "plus" then
Use the word "plus" or the "+" symbol or say "add and "
+ can be added. These are like terms. Adding them, with the square root and the i can be a little confusing at first. So I will first review the official way to add 6x and 13x and then use the same steps to add our expression.
6x + 13x
Although you probably know that the sum is 19x, this is the official way to do it:
Factor out the GCF
Add like terms in the "non-GCF" factor.
(6+13)x
19x
Using this same procedure on your expression: +
The GCF is :
(