Question

how do i simplify the square root of 81c^5,d^4

Answer 1

\[\sqrt{81}=9\]
\[\sqrt{c^5}=c^2\sqrt{c}\]
\[\sqrt{d^4}=d^2\] mash them up

Answer 2

so 9c^2square root of c d^2

Answer 3

i would write as
\[9c^2d^2\sqrt{c}\]
here is a more modern version
http://www.youtube.com/watch?v=Cw6pQUa0yS8&feature=related

Answer 4

thank you and i still need some help on this stuff are you willing ?

Answer 5

although i prefer the prince buster version

Answer 6

suer post away

Answer 7

ok so simplify the square root of 124y^6w^7

Answer 8

ok step by step. first the easy one. what is
\[\sqrt{y^6}\]?

Answer 9

y^2?

Answer 10

no. how many times does 2 go in to 6?

Answer 11

3

Answer 12

that is , what is 6 divided by 2
right, 3
so
\[\sqrt{y^6}=y^3\] because we know
\[(y^3)^2=y^6\]

Answer 13

now how about
\[\sqrt{w^7}\] in this case 2 does not divide 7 evenly, but it goes in to 7 3 times with a remainder of 1, so
\[\sqrt{w^7}=w^3\sqrt{w}\]

Answer 14

since 2 goes in to 7 3 times, w cubed comes out, one w stays in. for another example
\[\sqrt{x^{23}}=x^{11}\sqrt{x}\]

Answer 15

oh got that part!

Answer 16

finally
\[\sqrt{124}\] now
\[124=4\times 31\] so
\[\sqrt{124}=\sqrt{4\times 31}=\sqrt{4}\times \sqrt{31}=2\sqrt{31}\]

Answer 17

you don't need to write all the steps , that is just an explanation

Answer 18

so 2square root of 31y^3w^3square root w

Answer 19

put together get
\[\sqrt{124y^6w^7}=2y^3w^3\sqrt{31w}\]

Answer 20

put everything outside the radical first, then the radical with what is left inside

Answer 21

got it thanks

Answer 22

so now simplify the square root of 18/x^3

Answer 23

well, this one is a little different because you have to get the
\[\sqrt{x^3}\] out of the denominator

Answer 24

ok and how do i do that?

Answer 25

but even before we begin we can write
\[\sqrt{\frac{18}{x^3}}=\frac{\sqrt{18}}{\sqrt{x^3}}\] that part is ok right?

Answer 26

yes

Answer 27

and now from before we know
\[\sqrt{18}=\sqrt{9\times 2}=3\sqrt{2}\]

Answer 28

similarly
\[\sqrt{x^3}=x\sqrt{x}\]

Answer 29

leaving us with
\[\frac{3\sqrt{2}}{x\sqrt{x}}\]

Answer 30

now to get the radical out of the denominator you write the following
\[\frac{3\sqrt{2}}{x\sqrt{x}}=\frac{3\sqrt{2}}{x\sqrt{x}}\times \frac{\sqrt{x}}{\sqrt{x}}=\frac{3\sqrt{2x}}{x^2}\]

Answer 31

now there is no radical in the denominator. hope steps are clear

Answer 32

very thank you

Answer 33

how do i simplify 3/5-the squaer root of 2