Question

http://prntscr.com/hbc04f

Answer 1

1,2,4

Answer 2

A rational number is where it is a whole number or a decimal with repeating decimal such as 3.222222... and fractions (that either end nicely or repeat).

A. Shows \(\bf{\sqrt{11} \times \sqrt{5} = \sqrt{11 \times 5} = \sqrt{55}}\)
This would not be rational since the square root equals `7.416198487...`

Answer 3

i thought it was anynumber that was not whole

Answer 4

Irrational is `any number that can not be a rational number` such as \(\bf{\pi}\), \(\bf{\sqrt{8}}\), \(\bf{-\sqrt{11}}\) etc.

Answer 5

Rational are either repeated decimals, some fractions (that either end repeated or end nicely), and whole numbers.

Answer 6

oh

Answer 7

B. \(\bf{\sqrt{9} \times \sqrt{16} = \sqrt{9 \times 16} = \sqrt{144}}\)

The \(\bf{\sqrt{144}}\) squares easily to `12` so this is rational.

Answer 8

5rad4 is C?

Answer 9

Not quite. \(\bf{\sqrt{2} \times \sqrt{2} = 2}\)

So we end up with \(\bf{5 \times 2 =10}\)

Answer 10

10 is rational

Answer 11

yup

Answer 12

d is rational?

Answer 13

Well if we did \(\bf{3} \times \sqrt{2} = \sqrt{6}\) we have no term that squares perfectly from 6, so no.

Answer 14

oof im bad at radicals

Answer 15

Sorry meant \(\bf{\sqrt{3}}\)

Answer 16

Do you know your perfect squares?

Answer 17

i have a list of only 16

Answer 18

You can identify your perfect squares by taking a number and raising it to the power of 2.

\(\bf{1^{2}=1}\)
\(\bf{2^{2}=4}\)
\(\bf{3^{2}=9}\)
\(\bf{4^{2}=16}\)
\(\bf{5^{2}=25}\)
\(\bf{6^{2}=36}\)

so on and so forth...

Answer 19

For example let us say we have \(\bf\sqrt{54}\). We list the terms of `54` to see if it contains a perfect square.

`54:1,2,3,6,9,18,27,54,`

We see that it has `9` which is perfect, and we multiply `9` by `6` to get 54. So we turn it into this...

\(\large\bf{\sqrt{54} \rightarrow \sqrt{9 \times 6}}\)

Now we know that `9` is perfect but to what? Well it is `3` since it squares to this the term will be placed on the outside.

\(\large\bf{\sqrt{9 \times 6} \rightarrow 3\sqrt{6}}\)

This is the rational form of \(\bf{\sqrt{54}}\).

Answer 20

Do you kinda get the explanation?