Question

can u please help me with irrational square roots!!!

Answer 1

@iGreen

Answer 2

@pooja195

Answer 3

@sammixboo

Answer 4

@Holly00d1248

Answer 5

here are your steps:
\[\sqrt {134} = \sqrt {144 - 10} = \sqrt {144\left( {1 - \frac{{10}}{{144}}} \right)} = 12\sqrt {1 - \frac{{10}}{{144}}} \]

Answer 6

now we can use this approximation:
\[\sqrt {1 - \frac{{10}}{{144}}} \cong 1 - \frac{{10}}{{288}}\]

Answer 7

so we can write:
\[\sqrt {134} = 12\left( {1 - \frac{{10}}{{288}}} \right) = ...?\]

Answer 8

what do i do with the 10/288 divide?

Answer 9

@iambatman

Answer 10

because I used this approximation:
\[\sqrt {1 - a} \cong 1 - \frac{a}{2}\]
which is valid for all real numbers

Answer 11

ok but i dont understand what do i do multiply,divide or what?

Answer 12

I have started from 134= 144-10

Answer 13

that is a simple numeric identity

Answer 14

is it ok?

Answer 15

im sorry im confused i know 144-10 is 134 but what do i do?

Answer 16

we did it in order to apply the approximation that I wrote before

Answer 17

im confused i dont know what to write with all those numbers

Answer 18

soo its 1-a/2

Answer 19

yes! it is only a formula which we can apply to our computation when we need of it:
\[\sqrt {1 - a} \cong 1 - \frac{a}{2}\]

Answer 20

it is valid for those values of "a" such that a<1

Answer 21

and the quantity 10/144 is less than 1