– English Lyrics

Lyrics & Translation

[English]

we are given this expression with so

many square roots and our job is to make

this ratio into a more simpler form so

can you do it first we rewrite the

square < TK of 9 as theare < TK of 3 * <

TK 3 and the square < TK of 15 as Square

< TK of 3 * Square < TK of 5 similarly

we can rewrite the square otk of 12 in

the denominator as Square < TK of 4 * <

TK of 3 which simplifies to 2 * Square <

TK of 3 now this Square < TK of 1 will

simply be equal to 1 great next we

observe that the numerator contains

terms that can be grouped the terms

Square < TK of 3 + sare < TK of 5 remain

the same while from this part we can

take Square < TK of 3 as common to get

square < TK of 3 * Square < TK 3 + < TK

5 wow the numerator factors out as 1

plus the square < TK of 3 * theare < TK

of 3 plus the square < TK of 5 for the

denominator we rearrange the terms 1 + <

TK 5 + 2 * < TK 3 as 1 + < TK of 3 + <

TK of 3 + < TK of

5 noise let us call this fraction as a

variable X now here comes the magic if

this is X then 1 /x will be this right

let us simplify it to do so we split the

fraction into two separate terms the

first term is 1 + sare < TK of 3 / this

which simplifies to 1 / < TK 3 + < TK 5

the second term is square < TK 3 + < TK

of 5 divided by this which simplifies to

1 / 1 + < TK of 3 as a next step we will

rationalize each term separately to

rationalize 1 ided by square < TK of 3 +

< TK of 5 we multiply both the numerator

and denominator by sare < TK 5 - < TK 3

use a + b * a - b = a s - b square here

to get this denominator as 5 - 3 or 2 so

1 / < TK of 3 + < TK 5 simplifies to <

TK

5- < TK 3 / 2 similarly to rationalize 1

/ 1 + < TK 3 we multiply both numerator

and denominator by square < TK of 3 - 1

again using this we get this denominator

as 3 - 1 or 2 so this simplifies to

square root of 3 -1 / 2 Now by adding

these two results since the denominators

are the same we combine the numerators

to obtain this oh look Square < TK of 3

gets cancelled out and we are left with

< TK of 5 - 1 / 2 as 1 /x so x = 2 over

the < TK of 5 -1 we will rationalize

this one last time by multiplying both

numerator and denominator by theare < TK

of 5 + 1 again using this we get the

denominator as 5 - 1 or 4 this two gets

canceled out with four and we get x = 1

+ < TK 5 / two this is giving me

goosebumps and I am in shock right now

because this number is equal to none

other than the well-known golden ratio

which is a special number that appears

in nature

art and Mathematics so all this ugly

looking square roots simplify to this

beautiful golden racio if you enjoyed

this video please don't forget to like

share and subscribe to our channel so

good

[Music]

Key Vocabulary

Vocabulary	Meanings
square /skwɛər/ B1	noun - a plane figure with four equal sides and right angles verb - to multiply a number by itself
root /ruːt/ B1	noun - the square‑root of a number
ratio /ˈreɪʃi.oʊ/ B2	noun - a relationship between two numbers showing how many times the first contains the second
simplify /ˈsɪmplɪfaɪ/ B2	verb - to make something less complex or easier to understand
numerator /ˈnjuːməreɪtər/ C1	noun - the top part of a fraction that indicates how many parts are taken
denominator /dɪˈnɒmɪneɪtər/ C1	noun - the bottom part of a fraction that shows into how many equal parts the whole is divided
fraction /ˈfrækʃən/ B2	noun - a number expressed as a numerator divided by a denominator
variable /ˈvɛriəbəl/ B2	noun - a symbol that represents an unknown or changeable quantity
rationalize /ˈræʃənəˌlaɪz/ C1	verb - to eliminate a radical from a denominator by multiplying by its conjugate
multiply /ˈmʌltɪplaɪ/ B1	verb - to increase a number by repeatedly adding it to itself
cancel /ˈkænsəl/ B1	verb - to remove a common factor from a fraction or expression
golden /ˈɡoʊldən/ B2	adjective - relating to the golden ratio; valuable or splendid
nature /ˈneɪtʃər/ A2	noun - the physical world and its phenomena
art /ɑːrt/ A2	noun - creative expression produced through skill and imagination
mathematics /ˌmæθəˈmætɪks/ B2	noun - the abstract science of number, quantity, and space
ugly /ˈʌgli/ A1	adjective - unpleasant to look at; not attractive
beautiful /ˈbjuːtɪfəl/ A1	adjective - pleasing to the senses or mind; attractive
magic /ˈmædʒɪk/ A2	noun - the power of apparently influencing events using mysterious forces
observe /əbˈzɜːrv/ B1	verb - to watch carefully, especially with attention to details
rewrite /riːˈraɪt/ B1	verb - to write something again, typically in a different form or style