Question

Will give brainliest!!!!! Please help
Explain the differences between adding and multiplying radical expressions using 2 examples you create.

Please explain it in an easy way to understand because everyone else made it sound complicated with a lot of symbols

Answer 1

A radical expression is an expression that includes the root of some quantity. This can be a square root but it can be a cubed root or fourth root for example. Here are some examples:

$\sqrt{5}, 3 \sqrt{7} , 5 \sqrt{7}, -4 \sqrt{10}$

Multiplying Radicals
When we multiply two radical expressions you basically do this: multiply the numbers outside the radicals by each other and keep them outside the radical in the answer. Multiply the numbers under the radicals together and keep them under the radical sign in you’re answer. Simplify the radical in your answer if at all possible.

Let’s try it: $( \sqrt{5})(3 \sqrt{7})=3 \sqrt{35}$

Another example: $(5 \sqrt{8})(3 \sqrt{8})=15 \sqrt{64}=(15)(8)=120$


Adding Radicals
Adding radical is similar to adding expressions like 3x +5x. You need to have “like terms”. This means that we can only combine radicals that have the same number under the radical sign. When we add we add the numbers on the outside and keep that sum outside in our answer. We leave the number under the radical alone and include it in our answer just as it was.

Two examples:

$5 \sqrt{3}+7 \sqrt{3}=12 \sqrt{3}$

$-4 \sqrt{8}+2 \sqrt{8}=-2 \sqrt{8}$

If the number under the radical sign is different then you can’t combine them.

$3 \sqrt{5}+4 \sqrt{8}$ has to be left alone. You can’t combine them. It’s the same as 3x +4y you just leave them alone.

If you want a bit of vocabulary the number under the radical is called the radicand.