OpenStudy (love10129151):

can someone help me explain these questions

4 years ago
OpenStudy (love10129151):

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

4 years ago
OpenStudy (love10129151):

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

4 years ago
OpenStudy (love10129151):

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

4 years ago
OpenStudy (love10129151):

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

4 years ago
OpenStudy (love10129151):

please help explain it

4 years ago
OpenStudy (love10129151):

@zepdrix

4 years ago
zepdrix (zepdrix):

\[\Large\bf\sf \color{royalblue}{27)} -2\sqrt{7x ^{2}}\cdot\frac{1}{3}\sqrt{28x ^{3}}\]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,\[\Large\bf\sf \color{royalblue}{27)} -\frac{2}{3}\sqrt{7x^2\cdot 28x ^{3}}\]

4 years ago
zepdrix (zepdrix):

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

4 years ago
OpenStudy (love10129151):

yes

4 years ago
OpenStudy (love10129151):

@zepdrix

4 years ago
zepdrix (zepdrix):

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?

4 years ago
zepdrix (zepdrix):

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

4 years ago
OpenStudy (love10129151):

\[x^{6}\]

4 years ago
zepdrix (zepdrix):

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

4 years ago
zepdrix (zepdrix):

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

4 years ago
OpenStudy (love10129151):

oo sorry

4 years ago
zepdrix (zepdrix):

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?

4 years ago
zepdrix (zepdrix):

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

4 years ago
OpenStudy (love10129151):

ok

4 years ago
zepdrix (zepdrix):

What's the square root of 196?

4 years ago
OpenStudy (love10129151):

its 14

4 years ago
zepdrix (zepdrix):

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?

4 years ago
OpenStudy (love10129151):

no

4 years ago
zepdrix (zepdrix):

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,\[\Large\bf\sf \color{royalblue}{27)} -\frac{2\cdot14}{3\cdot1}\sqrt{x^5}\]

4 years ago
OpenStudy (love10129151):

ok

4 years ago