Question

What is the smallest integer lager than

Answer 1

\[\huge(\sqrt{3}+\sqrt{2})^6\]

Answer 2

Let the integer be x. than

\((\sqrt{3}+\sqrt{2})^6<x\)

Answer 3

First of all solve this inequality than all the values larger than the equation will be x. the smallest integer of x will be ur answer :)

Answer 4

\[ {x}^{1/6} >\sqrt{3}+\sqrt{2}\]

Answer 5

\[x^{1/3}>3+2\sqrt{6}+2=5+2\sqrt{6}>9\]

Answer 6

\[x>\sqrt[3]{9}>\sqrt[3]{8}=2\]

Answer 7

@jiteshmeghwal9

Answer 8

ok now wht do u think the value of x is ?

Answer 9

isn't two the one

Answer 10

i think u have to expand of (sqrt(2) + sqrt(3))^6, first..

Answer 11

\[=(5+2\sqrt{6})^3=125+3(25)2\sqrt{6}+3(5)24+8(\sqrt{6^3})\]

Answer 12

yes, = ... + ...*sqrt(6)

Answer 13

and finally u just take a smallest integer number of the result above

Answer 14

dont forget use ur calculator to get the value of sqrt(6) :)

Answer 15

\[485+125\sqrt{6}+8\sqrt{6}^3\]
\[\sqrt{6}>2\]
\[>485+125(2)+8(2^3)=799\]

Answer 16

hmmm..
485 + 3(25)2√(6) + 3(5)24 + 8*(√((6)^3)
= 125 + 150√(6) + 360 + 8*6√(6)
= 485 + (150+48)√(6)
= 485 + 198√(6)
= 485 + 484.99
= 969.99

Answer 17

so, the smallest integer number than 969.99 is 970

Answer 18

no calculator is allowed here

Answer 19

i think u can determine the value of sqrt(6) without calculator, right ?

Answer 20

just remember that :
sqrt(4) < sqrt(6) < sqrt(9)
2 < sqrt(6) < 3
so, sqrt(6) = 2.(.......), u can take nearst 2 decimals form

Answer 21

so 485+125(3)+8(sqrt6)^(3)
485+125(3)+8(3^3)=1076

Answer 22

970 is smallest than 1076 :p

Answer 23

*

Answer 24

* means

Answer 25

* means I bookmarked the question. Now whenever there is a post on the topic, I'll get a notification.

Answer 26

cool so how do I bookmark a question

Answer 27

do I just post the asteric *

Answer 28

o.O

* was just a symbol of bookmark,I could have made any other comment also over here for the notification thing. I chose *

Answer 29

485 + 198√(6)
Now, I would use NEWTON's METHOD to find its approxmiate value.
Let x=198√(6)
x^2=198*198*6
x^2=235224
x^2-235224=0
f(x)=0

Answer 30

I hope u can do it