Question

What is the exact value of the square root of 28 over 9 the square root of 16.? Simplify if possible.

Answer 1

\[\frac{\sqrt{28}}{9\sqrt{16}}\]

Answer 2

yes

Answer 3

You already know the square root of 16. What is it?

Answer 4

um 8?

Answer 5

oops 4

Answer 6

Okay, so now you have

\[\frac{\sqrt{28}}{9 \dot\ 4}\]

Answer 7

um 36

Answer 8

\[\frac{\sqrt{28}}{36}\]

Answer 9

Now think of two numbers that multiply to get 28. One of those numbers needs to be a perfect square.

Answer 10

um 2 and 14

Answer 11

Neither of those numbers are a perfect square.

Answer 12

okk?

Answer 13

So think of two other numbers.

Answer 14

7 and 4

Answer 15

Do you know which one of those are a perfect square?

Answer 16

4

Answer 17

Do you know why it is 4?

Answer 18

because 2 goes in it evenly

Answer 19

Because, in general:

`A perfect square is a number such that n x n = n^2, with n^2 being the perfect number.`

Answer 20

okkkaaayyy :)

Answer 21

Anyway, so now we can re-write the fraction like so:

\[\frac{\sqrt{4 \dot\ 7}}{36}\]

Answer 22

One rule of radicals states the following:

`The square root of a x b equals the square root of a times the square root of b:`
\[\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\]

Knowing this, how can we re-write the numerator?

Answer 23

i dont know? :(

Answer 24

oh wait would it be sqrt7 and sqrt 4?

Answer 25

\[\frac{1}{9}\sqrt{\frac{28}{16}}=\frac{1}{9}\sqrt{\frac{7}{4}}=\frac{\sqrt{7}}{18} \]

Answer 26

Yes, correct, so

\[\frac{\sqrt{4} \dot\ \sqrt{7}}{36}\]

Answer 27

ok

Answer 28

Now, you know the square root of 4. What is it?

Answer 29

2

Answer 30

So now, we have,

\[\frac{ 2\sqrt{7}}{36}\]

Answer 31

oookkk

Answer 32

We can rewrite 36 as 2 x 18 to get

\[\frac{ 2\sqrt{7}}{2 \dot\ 18}\]

Answer 33

Now what can we cancel in that fraction above?

Answer 34

sqr7 over 18!!! thank you!!!!!! <333

Answer 35

You cancel 2/2 to get the answer you mentioned, yet