Merasionalkan Penyebut Pecahan Bentuk Akar (1) - Matematika Kelas 9
Summary
TLDRIn this educational video from Angeles channel, the focus is on rationalizing the denominator of radical expressions, specifically the form \( \sqrt{a} \) and \( \sqrt{b} \). The method involves multiplying both the numerator and denominator by the conjugate of the denominator. The video explains three types of radicals and provides a step-by-step guide to simplify expressions like \( \frac{a+b}{\sqrt{c}} \). Examples are worked through, demonstrating how to simplify radical expressions by multiplying with conjugates and aiming for a square root in the denominator. The host encourages viewers to watch the entire video, subscribe, and engage with the content for a comprehensive understanding of rationalizing radical denominators.
Takeaways
- 📚 The video discusses the process of rationalizing the denominator of a radical fraction.
- 🔢 Rationalization involves multiplying both the numerator and the denominator by the conjugate of the denominator.
- 📐 There are three types of radical expressions: \( \sqrt{a} \), \( \sqrt{b} \), and \( \sqrt{a+b} \), and \( \sqrt{a-b} \).
- 📝 The conjugate of the denominator is crucial for the rationalization process, and it is formed by pairing the radical with its corresponding root.
- 📖 The video provides a step-by-step guide to understanding and performing the rationalization of radicals.
- 📐 The script includes examples to illustrate the process, such as rationalizing \( \frac{4\sqrt{5}}{\sqrt{5}+4\sqrt{5}} \) and \( \frac{\sqrt{3}}{\sqrt{6}} \).
- 🔑 The video emphasizes the importance of simplifying the result by looking for perfect square factors within the radicals.
- 🎯 The video aims to be educational, particularly for those interested in learning mathematics.
- 💡 The presenter encourages viewers to watch the entire video for a complete understanding and not to skip any part.
- 🌐 The video is part of a series, with the next installment focusing on rationalizing the denominator of the form \( \sqrt{a+b} \) and \( \sqrt{a-b} \).
Q & A
What is the main topic discussed in the video?
-The main topic discussed in the video is rationalizing the denominator of radical expressions, specifically focusing on the form 'a per square root of b'.
What is the method used to rationalize the denominator of a radical expression?
-The method used to rationalize the denominator of a radical expression is to multiply both the numerator and the denominator by the conjugate of the denominator.
What are the three types of radical expressions mentioned in the video?
-The three types of radical expressions mentioned are 'a per square root of b', 'c per square root of a plus minus square root of b', and 'a plus minus square root of b'.
What does the term 'conjugate' refer to in the context of rationalizing denominators?
-In the context of rationalizing denominators, 'conjugate' refers to the expression that is formed by changing the sign of the radical part of the denominator.
How does the video suggest simplifying the expression 'a square root of b per square root of d'?
-The video suggests simplifying the expression 'a square root of b per square root of d' by multiplying it with the conjugate of the denominator, which is 'square root of b', resulting in 'a square root of b times square root of d'.
What is the purpose of multiplying by the conjugate in the rationalization process?
-The purpose of multiplying by the conjugate in the rationalization process is to eliminate the radical from the denominator, making the expression easier to work with.
Can you provide an example of rationalizing a denominator from the video?
-An example from the video is rationalizing the expression '4 per square root of 5'. The conjugate of the denominator 'square root of 5' is 'square root of 5', and multiplying the numerator and denominator by this conjugate results in '4 square root of 5 per square root of 25', which simplifies to '5'.
What is the significance of having a perfect square in the rationalization process?
-Having a perfect square in the rationalization process is significant because it allows for the radical to be simplified, making the expression more manageable.
How does the video handle the simplification of radicals in the denominator?
-The video handles the simplification of radicals in the denominator by multiplying the numerator and denominator by the conjugate and then simplifying by combining like terms and reducing the radicals to their simplest form.
What is the final step in rationalizing the denominator according to the video?
-The final step in rationalizing the denominator, as per the video, is to simplify the resulting expression by reducing any radicals that are perfect squares and combining like terms.
Outlines
📘 Rationalizing Radical Expressions Part 1
This paragraph introduces a tutorial on rationalizing the denominator of radical expressions, specifically focusing on the form 'a + b√c'. The process involves multiplying both the numerator and the denominator by the conjugate of the denominator. The video emphasizes the importance of understanding the three types of radicals: 'a√b', 'a+b√c', and 'a-b√c'. It encourages viewers to watch the entire video for a comprehensive understanding and not to skip any part. The tutorial also invites viewers to subscribe, activate notifications, and share the video on social media. Practical examples are given to demonstrate the process of rationalizing expressions, such as '4√5' and '√3/√6', with step-by-step simplifications shown.
🔢 Simplifying Radical Expressions
The second paragraph continues the tutorial by illustrating how to simplify radical expressions further. It provides an example of simplifying '2√6/3√2' by multiplying the scalar in front of the radical with the radical itself. The process involves simplifying the expression by combining like terms and looking for perfect square factors to simplify the radicals. The example provided walks through the steps of simplifying '2√6/3√2' to '6√2/3√6' and then further to '9√2/3√36'. The final simplification results in '9√2/18', which is then rationalized to '3√2/6'. The paragraph concludes with a prompt for viewers to comment if they have any questions and a teaser for the next video, which will cover rationalizing the form 'a + b√c'.
Mindmap
Keywords
💡Rationalize
💡Radical
💡Denominator
💡Numerator
💡Conjugate
💡Square Root
💡Multiplication Property of Radicals
💡Simplify
💡Real Numbers
💡Coefficient
💡Quadratic Radical
Highlights
Introduction to rationalizing the denominator of radical expressions.
Explanation of multiplying the numerator and denominator by the conjugate of the denominator.
Three types of radical expressions: a√b, c√a+b, and a+b√c.
The conjugate of the denominator is the radical of the denominator itself.
Example of rationalizing the expression 4√5/√5.
Multiplication of the numerator and denominator by the conjugate to eliminate the radical.
Result of rationalizing 4√5/√5 is 5/1.
Example of rationalizing √3/√6 using the conjugate method.
Multiplication of radicals and simplification to get √18/√6.
Further simplification to express √18 as 3√2.
Final result of rationalizing √3/√6 is 3√2/6.
Simplification of the expression 3√2/6 to 1/2√2.
Example of rationalizing 2√6/3√2 using scalar multiplication.
Multiplication of scalars and radicals to get 6√2/3√2.
Final simplification of 6√2/3√2 to 2√3.
Encouragement to watch the entire video for a complete understanding.
Call to action for viewers to subscribe, activate notifications, and share the video.
Anticipation for the next video discussing rationalizing the denominator of the form a+b√c.
Transcripts
Halo Bismillahirohmanirohim
Assalamualaikum warahmatullahi
wabarakatuh Selamat datang kembali di
Angeles channel pada video kali ini kita
akan membahas tentang merasionalkan
penyebut pecahan bentuk akar part1 yaitu
bentuk aper akar B merasionalkan
penyebut pecahan bentuk akar dilakukan
dengan cara mengalikan pembilang dan
penyebut pecahan tersebut dengan
pasangan bentuk akar Sekawan penyebutnya
secara umum ada tiga macam pecahan
bentuk akar yaitu a per akar b c per
aplus minus akar b c berakar a-plus
minus akar B agar benar-benar faham
silahkan simak video pembahasannya
sampai tuntas dan jangan diskip ya keep
your watching
Hai namun sebelum lanjut silakan klik
subscribe terlebih dahulu kemudian
aktifkan notifikasinya dan jangan lupa
like and share ke media sosial kalian
semoga video ini bisa bermanfaat dan
semakin banyak yang mau belajar
khususnya belajar matematika
merasionalkan bentuk apel akar B
dilakukan dengan cara mengalikan
penyebut dan pembilang nya dengan bentuk
Sekawan penyebutnya penyebutnya adalah
akar b maka sekawannya adalah akar B
sehingga affair akar b = a per akar B
dikali akar B per akar d = a akar B per
b = a + b akar B dimana a&d bilangan
real Oke agar lebih paham Mari kita
lanjut ke contoh soal misalkan
Hai rasionalkanlah bentuk pecahan
berikut penyelesaiannya point A4 per
akar 5 per hatikan menyebutnya yaitu
akar5 maka bentuk Sekawan dari penyebut
nya adalah akar 5 Plus dengan empat per
akar 5 dikalikan akar 5 per akar 5 Plus
dengan empat kali akar 5 Plus silnya 4
akar 5 per akar 5 dikalikan akar 5 Plus
silnya akar 25 = 4 akar 5 per akar 25
hasilnya 5 =
the point B akar 3 per akar 6 Bentuk
Sekawan dari penyebut nya adalah akan
enam Maka = akar 3 per akar 5 dikalikan
akar 6 per akar 6 = akar 3 dikali akar 6
hasilnya akar 18 perakaran 6 dikali akar
6 hasilnya akar 36 kemudian akan 18 kita
Sederhanakan lagi dengan sifat perkalian
bentuk akar yaitu mengubahnya menjadi
perkalian faktornya dan usahakan salah
satu faktornya merupakan akar kuadrat
terbesar = akar sembilan dikali akar 2
per akar 36 hasilnya 6 = akar rubilane
hasil
MP3 lalu kalikan dengan akar dua
hasilnya tiga Akar dua pernah sama
dengan Sederhanakan 3/6 menjadi 1 per 2
akar 2 lanjut poin terakhir yaitu point
C2 akar 6/3 akar dua bentuk Sekawan dari
penyebut nya adalah tiga Akar dua
sehingga = 2 akar 6 pertiga akar2 dikali
tiga Akar Dua pertiga akar2 kemudian
kalikan bilangan skalar atau angka yang
ada di depan bilangan bentuk akar dengan
bilangan skalar dan bilangan bentuk akar
dengan bilangan bentuk akar
Hai sama dengan dua kali tiga hasilnya
6-akar enam kali akar dua hasilnya akar
12 per tiga kali tiga hasilnya 9 akar
dua kali akar dua hasilnya akar 4 lanjut
akan 12 Sederhanakan lagi dengan sifat
perkalian = 6 akar empat kali akar 3 per
sembilan kali akar 4 hasilnya dua
ditulis dalam kurung 2 Tanda kurung
menandakan perkalian = 6 turunkan aja
akar 4 hasilnya dua ditulis dalam kurung
2 kali akar 3 per sempit
dan kali dua hasilnya 18 sama dengan 6
kali dua hasilnya 12 kali akar 3 per
delapan belas = Sederhanakan 12/18
menjadi 2/3 akar 3 oke teman-teman
demikian pembahasan tentang
merasionalkan penyebut pecahan bentuk
akar part1 semoga bermanfaat Jika ada
yang kurang paham silahkan komen di
kolom komentar sampai ketemu lebih di
pertemuan berikutnya yaitu pembahasan
tentang merasionalkan penyebut pecahan
bentuk akar part 2 yaitu merasionalkan
bentuk ceper akar a plus minus akar B
terima kasih wassalamualaikum
warahmatullahi wabarakatuh bye
Transformers hmm hmm
تصفح المزيد من مقاطع الفيديو ذات الصلة
Asinkronus Topik Bentuk Akar W 2
Simplifying Radicals With Variables, Exponents, Fractions, Cube Roots - Algebra
Adding and Subtracting Rational Expressions With The Same Denominators
SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSION || GRADE 8 MATHEMATICS Q1
Limits of functions | Calculus
How to Multiply Two Fractions | Multiplying Fractions
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