Question

Algebra Questions :)

1. Simplify 4 square root 6 divided by square root 30 by rationalizing the denominator. Show your work.

Answer 1

\[\frac{ 4\sqrt{6} }{ \sqrt{30} }\]

Answer 2

@calculusxy Yes

Answer 3

So we need to first find the square root of 30.

Answer 4

Square root of 30 = 5.4 @calculusxy

Answer 5

\(30=5\cdot 6\quad \quad \Longrightarrow\quad\quad\sqrt{30}=\sqrt{5\times 6}=\sqrt{~5~}\times \sqrt{~6~}\)

Answer 6

And then, you know that in general,

\(\color{#000000 }{ \displaystyle \frac{a\times b }{c\times b} =\frac{a\times \bcancel{b} }{c\times \bcancel{b} }=\frac{a}{c} }\)

Answer 7

To rationalize the denominator (which is what this question asks you to do), you multiply the top and bottom of the fraction by the denominator to get rid of the radical. For example:\[\frac{ a }{ \sqrt{b} }\] You can rationalize this by multiplying by the denominator over itself:\[\frac{ a }{ \sqrt{b} }=(\frac{ a }{ \sqrt{b} })(\frac{ \sqrt{b} }{ \sqrt{b} })\] This gets rid of the radical in the denominator, then you simplify:\[(\frac{ a }{ \sqrt{b} })(\frac{ \sqrt{b} }{ \sqrt{b} })=\frac{ a \sqrt{b} }{ b }\] Use that strategy here to simplify.

Answer 8

you got to hate these smiles :)