Question

Simplify the radical expression.
sqrt of 7 (sqrt of 14 + sqrt of 3)
please show the steps

Answer 1

\[\sqrt{7} + \sqrt{14} + \sqrt{3}\]

Answer 2

Is that what you have? @CalvinG

Answer 3

Sorry just learning how to use the interface. It is \[\sqrt{7}\left( \sqrt{14}+ \sqrt{3} \right)\].

Answer 4

Oh, so I would distribute the radical 7... which means you must multiply what is inside of the radicals. So can you tell me what you get?

Answer 5

So would it be \[\sqrt{7}\times \sqrt{14} and \sqrt{7}\times \sqrt{3}\]

Answer 6

Yes.

Answer 7

So what do you get?

Answer 8

\[\sqrt{98}+\sqrt{21}\]

Answer 9

Correct!

Answer 10

Is that the answer?

Answer 11

Now, we have to see if we can find a perfect square to go into 98 and then we can check if one goes into 21.

Answer 12

ok

Answer 13

Nope, that is not the answer. I found a perfect square that goes into 98. So lets see if you can find it.

Answer 14

\[7\times14\]

Answer 15

A perfect square as in ... 4 x 4 = 16
16 is the perfect square

Answer 16

Ok I am lost. How would you go about finding the perfect square of 98.

Answer 17

Okay, so @CalvinG, what you want to do is... lets say for instance we used the perfect square 16. You would then check to see if 16 goes into 98.

98 / 16 = 6.125 (So we know that is not correct. Since the perfect square must go in it evenly... also remember that means we used 4 x 4)

(So, try 5 x 5, 6 x 6, 7 x 7, etc... until one of the perfect squares goes into 98)

Answer 18

\[7\times7=49\] which is halve of 98?

Answer 19

Correct!

Answer 20

So what we have now is..

Answer 21

\[\sqrt{49 * 2}\]

Answer 22

So take the perfect square and square root it. Once you get the square root then that number must come on the outside of the radical. Which would then leave the non perfect number to stay under the radical. So can you tell me what you get?

Answer 23

\[7\sqrt{2}\]?

Answer 24

Yes!

Answer 25

Now we have..

\[7\sqrt{2} + \sqrt{21}\]

Answer 26

Can that 21 be broken down?

Answer 27

\[7\times3\]

Answer 28

What number there is perfect?

Answer 29

7

Answer 30

Nope.

Answer 31

3 x 3 = 9

9 is perfect

Answer 32

So would it be \[3\sqrt{7}\]

Answer 33

Nope

Answer 34

Remember you are looking for something like...

2 x 2 = 4

4 is perfect... so you would need to check to see if the 4 goes into 21

Answer 35

not perfectly

Answer 36

It must go into the 21 perfectly.

Answer 37

Sorry evenly is the word i was looking for. lol

Answer 38

so 21 can not be broken down?

Answer 39

Correct, 21 can not be broken. :)

Answer 40

so is \[7\sqrt{2}+\sqrt{21}\] as far as it can be simplifyed?

Answer 41

Yup

Answer 42

Thank you!