Question

can someone help me explain these questions

Answer 1

\[27. -2\sqrt{7x ^{2}}*\frac{ 1 }{ 3 } \sqrt{28x ^{3}}\]

Answer 2

\[33. (3\sqrt{2}-2\sqrt{5})(4\sqrt{2}+ 2\sqrt{5})\]

Answer 3

\[43. n \sqrt{2}=\sqrt{9-3n}\]

Answer 4

\[47. y=\sqrt{x+4}\]

Answer 5

please help explain it

Answer 6

@zepdrix

Answer 7

\[\Large\bf\sf \color{royalblue}{27)} -2\sqrt{7x ^{2}}\cdot\frac{1}{3}\sqrt{28x ^{3}}\]Multiplication is commutative, so we can multiply things in any order.
Let's bring the 1/3 to the front and multiply it with the -2.\[\Large\bf\sf \color{royalblue}{27)} -\frac{2}{3}\sqrt{7x ^{2}}\cdot\sqrt{28x ^{3}}\]Then we'll combine our square roots by multiplying the insides together,\[\Large\bf\sf \color{royalblue}{27)} -\frac{2}{3}\sqrt{7x^2\cdot 28x ^{3}}\]

Answer 8

From there we can multiply some stuff together under the root.
Following along so far?

Answer 9

yes

Answer 10

@zepdrix

Answer 11

So again, under the root we're multiplying so we can move stuff around.
We'll multiply the 7 and 28.
And then we'll multiply the x^2 by x^3.
What do the x's give you?

Answer 12

\[\Large\bf\sf x^2\cdot x^3\quad=\quad ?\]

Answer 13

\[x^{6}\]

Answer 14

No silly!
When we multiply terms of similar bases, we `add the exponents`.\[\Large\bf\sf x^2\cdot x^3\quad=\quad x^{2+3}\quad=\quad x^5\]

Answer 15

\[\Large\bf\sf \color{royalblue}{27)} -\frac{2}{3}\sqrt{7\cdot28x^5}\]

Answer 16

oo sorry

Answer 17

Multiplying the 7 and 28,
\[\Large\bf\sf \color{royalblue}{27)} -\frac{2}{3}\sqrt{196x^5}\]Now we need to ask ourselves, does 196 have any factors that are perfect squares?

Answer 18

Oh nevermind, 196 is itself a perfect square it seems! :)

Answer 19

ok

Answer 20

What's the square root of 196?

Answer 21

its 14

Answer 22

Ok good so we'll take the square root of 196,
\[\Large\bf\sf \color{royalblue}{27)} -\frac{2}{3}\cdot 14\sqrt{x^5}\]Then multiply the 14 by the -2/3,
do you understand how to do that?

Answer 23

no

Answer 24

You can think of \(\Large\bf\sf 14\) as \(\Large\bf\sf \dfrac{14}{1}\),

and then just do fraction multiplication,
\[\Large\bf\sf \color{royalblue}{27)} -\frac{2}{3}\cdot \frac{14}{1}\sqrt{x^5}\]
top with top,
bottom with bottom,\[\Large\bf\sf \color{royalblue}{27)} -\frac{2\cdot14}{3\cdot1}\sqrt{x^5}\]

Answer 25

ok