Question

Operations w/ Radicals help?

What is the exact value of the expression the square root of 294. - the square root of 24. + the square root 54.? Simplify if possible.

8 the square root of 2.

8 the square root of 6.

12 the square root of 2.

12 the square root of 6.

Answer 1

\[ \sqrt {294} - \sqrt{24} + \sqrt{54}\]
\[ \sqrt {49*6} - \sqrt{4*6} + \sqrt{9*6}\]

Answer 2

Can you see the next step?

Answer 3

I need to simplify the square roots right? :)

Answer 4

yup yup ^^

Answer 5

Alright, please don't go anywhere! I will solve this, and would you mind if you could check it? BUT like not tell me the answer just like give me tiny hints?

Answer 6

absolutely ^_^

Answer 7

So when simplifying the radical of a square root

\[\sqrt{a*b} = \sqrt{a}\sqrt{b}\]

Answer 8

\[\sqrt{7} * \sqrt{6} - \sqrt{2} * \sqrt{6} + \sqrt{3} * \sqrt{6}\]

Answer 9

close!! ^_^

for the first term

\[\sqrt{49*6}=\sqrt{49}\sqrt{6}=7\sqrt{6}\]

Answer 10

Ok, let me rewrite my answers

Answer 11

\[\sqrt{7}\sqrt{6} - \sqrt{2}\sqrt{6} + \sqrt{3}\sqrt{6}\]

Answer 12

\[ \text{Your leading coefficient of each term (the first past, ie,} \underbrace{\sqrt{7}}_{\hbox{this part}} \sqrt{6}\]

you're "square rooting" twice. When you pull the
\[\sqrt{49}\] out of the radical, it turns into

\[\sqrt{49}=7\]

Answer 13

~first part

Answer 14

Ok, I understand so far, continue. :)

Answer 15

\[7\sqrt{6}- 2\sqrt{6}+3\sqrt{6}\]
\[8\sqrt{6}\]

Answer 16

so
\[\sqrt{49*6} = \sqrt{49}\sqrt{6}=7\sqrt{6}\]
as opposed to what you had

\[\sqrt{49*6} = \sqrt{49}\sqrt{6}≠\sqrt{7}\sqrt{6}\]

Answer 17

each of the three terms follows that same rule
\[\sqrt{49*6} -\sqrt{4*6}+\sqrt{9*6}= \sqrt{49}\sqrt{6}-\sqrt{4}\sqrt{6}+\sqrt{9}\sqrt{6}\]

*that's when you can simplify each of the leading terms (which are all happy perfect squares ^_^)

Answer 18

and it simplifies to what @radar wrote above ^_^

Answer 19

Ok, I completely understand the simplifying now. Now, when I have the remaining ones like @radar wrote above, how should I solve it? :)

Answer 20

Then, since each of the terms have a common factor, you can factor out the
\[\sqrt{6}\]

\[7\sqrt{6}-2\sqrt{6}+3\sqrt{6}=(7-2+3)\sqrt{6}\]

Answer 21

So, then, I'd do 7 - 2, which is 5, and then add 3, which is 8, and then I'd get 8sqrt{6}

Answer 22

correct! ^_^

Answer 23

Thank you so much for the wonderful help! Quick question, if I wanted to ask you a question again, how would I do that? Should I contact you or something on here?