Math olympiad | Algebra | Simplify the surd expression | โˆš(๐Ÿ–+โˆš๐Ÿ”๐Ÿ‘) โˆ’โˆš(๐Ÿ–โˆ’โˆš๐Ÿ”๐Ÿ‘) | Can you solve ?

preview_player
ะŸะพะบะฐะทะฐั‚ัŒ ะพะฟะธัะฐะฝะธะต
Math olympiad | Algebra | Simplify the surd expression | โˆš(๐Ÿ–+โˆš๐Ÿ”๐Ÿ‘) โˆ’โˆš(๐Ÿ–โˆ’โˆš๐Ÿ”๐Ÿ‘) | Can you solve ?

This video discusses a famous problem on algebra taken from an olympiad. Surd Simplification problem

#mathematics
#maths
#mathsolympiadpreparation
#mathsolympiad
#mathematicsolympiad
#mathsquestion
#surds
#surds_and_indices
#simplification
  1. Mathofer
  2. maths problems
  3. maths olympiad problems
  4. us maths olympiad
  5. us olympiad
  6. olympiad problems
ะ ะตะบะพะผะตะฝะดะฐั†ะธะธ ะฟะพ ั‚ะตะผะต
Math Olympiad Question 0:07:26

Math Olympiad Question | Nice Algebra Equation | You should know this trick!!

Thailand | Math 0:01:26

Thailand | Math Olympiad Question | Nice Algebra Equation

How to get 0:07:01

How to get better at algebra for math competitions

Math Olympiad | 0:08:38

Math Olympiad | A Very Nice Algebra Problem

A beautiful international 0:01:00

A beautiful international math olympiad problem

France - Math 0:08:40

France - Math Olympiad Question | An Algebraic Expression | You should be able to solve this!

A nice Math 0:07:29

A nice Math Olympiad Algebra problem| Solve for y.

A Very Nice 0:08:22

A Very Nice Algebra Challenge | Math Olympiad Problem

Math Olympiad 5^x=x 0:08:03

Math Olympiad 5^x=x | A Nice Math Olympiad Algebra Problem

Russia| Math Olympiad|Algebra| 0:15:50

Russia| Math Olympiad|Algebra| Can you solve for the 4 values of x?

Math Olympiad 1^x 0:08:49

Math Olympiad 1^x = -2 | A Nice Math Olympiad algebra problem @MathOlympiad0

Poland ๐Ÿ‡ต๐Ÿ‡ฑ Math 0:07:33

Poland ๐Ÿ‡ต๐Ÿ‡ฑ Math Olympiad 1993 - Algebra - Functional Problem f(x)?!

Math Olympiad Practice 0:01:00

Math Olympiad Practice

A nice math 0:01:19

A nice math olympiad algebra problem | Olympiad mathematics (x)=?

Canada | Math 0:10:20

Canada | Math Olympiad | A Nice Algebra Problem

Luxembourg - Math 0:02:51

Luxembourg - Math Olympiad Question | You should know this trick

Math Olympiad Problem 0:09:51

Math Olympiad Problem | A Nice Algebra Challenge

Math Olympiad | 0:08:15

Math Olympiad | A Nice Algebra Problem #maths #algebra

Mathematical Olympiad | 0:15:56

Mathematical Olympiad | Algebra Problem | Math Olympiad Preparation

A Nice Olympiad 0:00:52

A Nice Olympiad Exponential Multiplication Problem #short #olympiad #mathematics #maths #exponents

When mathematicians get 0:00:37

When mathematicians get bored (ep1)

China | Math 0:10:37

China | Math Olympiad | A Nice Algebra Problem ๐Ÿ‘‡

Math Olympiad | 0:14:11

Math Olympiad | A Nice Algebra Problem ๐Ÿ‘‡

How to get 0:06:15

How to get better at Combinatorics for Math competitions and the International Math Olympiad?

ะšะพะผะผะตะฝั‚ะฐั€ะธะธ
ะะฒั‚ะพั€

Rather than square the whole expression and then run into the problem of whether to take a negative as well as a positive square root, you could simplify the two expressions under the outer square roots by using the identities
(a + b)^2 = a^2 + b^2 + 2ab and (a-b)^2 = a^2 + b^2 - 2ab.

sqrt (8 + sqrt63) - sqrt(8 - sqrt63)
= [sqrt (16 + 2 sqrt63)]/sqrt2 - [sqrt (16 - 2sqrt63)]/sqrt2
multiplied by 2 inside the sqrt sign; divided by sqrt2 outside
= [sqrt (9 + 7 +2 sqrt9.sqrt7)] /sqrt2 - [sqrt (9 + 7 - 2 sqrt9.sqrt7)]/sqrt2
= [sqrt (sqrt9 + sqrt7)^2]/sqrt2 - [sqrt (sqrt9 - sqrt7)^2]/sqrt2
= [sqrt9 + sqrt7]/sqrt2 - [sqrt9 - sqrt7]/sqrt2 Outer square root cancelled by square
= [sqrt9 + sqrt7 - sqrt9 + sqrt7]/sqrt2
= 2sqrt7/sqrt2 2/sqrt2 = sqrt2
= sqrt2.sqrt7
= sqrt14

faithlesshound