Question

Simplify -3√48 - 2√27

Answer 1

\[-3\sqrt{3*16} -2\sqrt{3*9}\]

Answer 2

...which is the same as:
\[-3\sqrt{16}\sqrt{3} - 2\sqrt{9}\sqrt{3}\]
...which is fairly trivial to simplify.

Answer 3

what...?

Answer 4

Well, I've shown you the first 2 steps. If you understand the first two steps, you'll understand how to solve most problems of this kind. However, there are 1 or two rules about roots that you need to know.

the first is that:
\[\sqrt{a}\sqrt{b} =\sqrt{ab}\]
the second is:
\[b \sqrt{a}+c \sqrt{a} = (b+c) \sqrt{a}\]

Answer 5

The first rule is very simple to understand, and quite intuitive if you think about it. For example, if a=3 and b=9, then:
\[\sqrt{4} \sqrt{9} = \sqrt{4*9}\]
which can be simplified to:
\[2*3 = \sqrt{36}\]

This is what I did in the first step... however, I went in the reverse direction and divided the roots in the equation into the
\[\sqrt{a} \sqrt{b}\]
form.

ie:
\[\sqrt{48} \rightarrow \sqrt{3*16} \rightarrow \sqrt{3} \sqrt{16}\]

Answer 6

sorry... meant a=4 in that first sentence of that last post....

Anyways, thats how I got the equation in my second post...by taking the roots and turning them into two seperate roots.

All that's needed is to then take the second rule and apply it to the equation in the second post to find the answer.

Answer 7

So:
\[-3 \sqrt{16} \sqrt{3} \rightarrow -4 (4) \sqrt{3} \rightarrow -16 \sqrt{3}\]
and:
\[-2 \sqrt{9} \sqrt{3} \rightarrow -2(3)\sqrt{3} \rightarrow -6 \sqrt{3}\]

Answer 8

Adding the two terms together should then give you your answer.

Answer 9

So:
\[-16 \sqrt{3} -6 \sqrt{3} = ?\sqrt{3}\]

Answer 10

Don't know how to make it clearer without directly giving you the answer... but taking the second rule I gave you, you should be able to figure out what number goes in place of the question mark.