Question

What is the exact value of (sqrt) 38 / 2 (sqrt) 6?

19 (sqrt) 57/ 6
2 (sqrt) 57 / 3
(sqrt) 57 / 3
(sqrt) 57 / 6

Answer 1

\[\sqrt{38} / (2\sqrt{6})\] is that your question?

Answer 2

Yes!

Answer 3

do you know what a conjugate is?

Answer 4

No...?

Answer 5

in easiest terms its a special fraction used to eliminate denominators of radicals and its always equivalent to unity (1)

Answer 6

in your case the denominator is \[2\sqrt{6}\] so the conjugate is \[\sqrt{6} / \sqrt{6}\] which is equal to one, we together?

Answer 7

Yes.

Answer 8

now multiply your question with the conjugate as follows which is the same as multiplying with one, so it'll not affect the value of your question but rearrange it as follows
\[\left\{\sqrt{38} /2\sqrt{6} \right\} * \sqrt{6} /\sqrt{6}\]
becomes:

Answer 9

\[(\sqrt{38} * \sqrt{6} ) /2\]

Answer 10

correction, it becomes \[(\sqrt{38} * \sqrt{6}) / 2*6\]

Answer 11

we together butter...

Answer 12

Yes

Answer 13

now multiply the two radicals 38 and 6 and you get \[(\sqrt{288} )/12\]

Answer 14

now from your choices i can see root 57, implying that it must be a factor of 288 i.e 288 = 57 *4 , right?

Answer 15

Right.

Answer 16

so \[\sqrt{288} = \sqrt{4} * \sqrt{57}\] but root 4 is equal to \[2\sqrt{57}\] are we toogether?

Answer 17

so we've managed to reduce the numerator and we can now simplify the expression: \[(2\sqrt{57}) / 12\]
divide 12 by 2 and get \[(\sqrt{57}) /6\]

Answer 18

Okay. Sorry this is a little confusing for me.

Answer 19

where you lost?

Answer 20

The part where root 4 becomes root 2.

Answer 21

we together there?