Anyone good with radicals?? i need help please!

Question

mathstudent55 · Answer

Where's the question?

anonymous · Answer

one second i will post them!

mathstudent55 · Answer

Ok.

anonymous · Answer

What is the product of $$5\sqrt{3}\times4\sqrt{15}$$ ? Simplify if possible.

anonymous · Answer

$$3\sqrt{7}\sqrt{7} \over 6\sqrt{7^{5}}$$

anonymous · Answer

$$\sqrt{7} \over ^{4}\sqrt{7}$$

anonymous · Answer

Then what is the exact value fr the expression $$\sqrt{56}-\sqrt{14}+\sqrt{126}$$

mathstudent55 · Answer

Let's look at the first one.

In general, 

$a\sqrt{b} \times c \sqrt{d} $

$ac\sqrt{bd} $

mathstudent55 · Answer

Multiply the numbers together and multiply the radicals together.

anonymous · Answer

aright so for the first one would it be $$20\sqrt{5}?$$

mathstudent55 · Answer

$ 5 \times 4\sqrt{3 \times 15} $ right?
Which gives you this:
$20 \sqrt{45} $

anonymous · Answer

Yes, that is exactly what i got, but  i think it needs to be simplified further. So it either has to be $$20\sqrt{5} $$ or $$20\sqrt{15}$$

anonymous · Answer

so its probably 20 (radical sign)15. Correct?

mathstudent55 · Answer

The root 45 needs to be simplified, but to simplify it you can't just toss a part of it away.

This is how it's done.
You need to look at 45 and see if it has a factor that is a perfect square.

45 = 9 * 5, and 9 is  a perfect square.

$20\sqrt{45} $

$= 20 \sqrt{9 \times 5} $

$= 20 \sqrt{9} \sqrt{5} $

$=20 \times 3 \times \sqrt{5} $

$=60\sqrt{5} $

mathstudent55 · Answer

The 45 factors into 9 times 5.
9 has a square root of 3 which is taken out.
3 times 20 is 60.

anonymous · Answer

Ohhhh! i missed that factoring step then because 45 can be factored.. I went ahead... thank you! can you help me with the rest? :)

mathstudent55 · Answer

$\Large{ 3\sqrt{7}\sqrt{7} \over 6\sqrt{7^{5}}}$

I suggest you rewrite each root as a power.

Remember that 

$ \Large a^{\frac{a}{b}} = \sqrt[b]{a}  $

anonymous · Answer

Ooo this one is a bit more confusing

mathstudent55 · Answer

$\Large{ 3 \times 7^{\frac{1}{2} } 7^{\frac{1}{2} } \over 6\times7^{\frac{5}{2} }}$

anonymous · Answer

$$7\frac{ 5 }{ 3 }$$ i might have simplified wrong.

mathstudent55 · Answer

$\Large{ 3 \times 7^{\frac{1}{2} } 7^{\frac{1}{2} } \over 6\times7^{\frac{5}{2} }}$

$= \Large \dfrac{1}{2} \times 7^{\frac{1}{2} + \frac{1}{2} - \frac{5}{2}} $

$= \Large \dfrac{1}{2} \times 7^{-\frac{3}{2}} $

$=\Large \dfrac{1}{2 \times 7^{\frac{3}{2}    } } $


$=\Large \dfrac{1}{2 \sqrt{7^3}  } $

anonymous · Answer

7?