MATHEMATICS FOR HIGH SCHOOL STUDENTS - SURDS

MATHEMATICS LECTURE FOR HIGH SCHOOL STUDENTS - SURDS.

Topic: SURD

Welcome everyone! This would be our first mathematics class and lecture the very first topic we will be looking out is "SURDS".
What is SURD? Surd is An irrational number, especially one expressed using the √ symbol.. They are several types of Surd [Multiplication of SURDS, Multiplication of SURDS involving brackets,Division Of SURDS] I would examples and solve them so you can comprehend..lets look at the rules of Surd.

 RULES OF SURDS.
👉 By putting m=9 and n=4,find which of the following pairs of expressions are equal.
1. √mn = √m × √n
2. √m+n = √m + √n
3. √m/n = √m ÷ √n
4. √m-n = √m - √n
5. 2√m = √2m
6.3√n = 1/√9n
As given above m=9 and n=4 so all we have to do substitute wherever you find m to 9 and wherever you find n to 4..simple as ABC... Check this number 1 out;
1. √MN = √m × √n
= √9 × √4 = √36
And finally the square root of 36 = 6. (final answer).
You guys should probably try the remaining 5 and send your answers to my email [amakagodisgood@gmail.com] or use the contact us page of this blog. Let's proceed.

 MULTIPLICATION OF SURDS.
👉 Simplify the following
1.) √5 x √10
= √5 x √5x2
=√5 x √5 x √2 (according to a rule of Surd any number in square root the same with another become the number without square root. Example √6 x √6 = 6. We applied it below 👇
= 5√2. (final answer).

2. √8 x √2
= √4x2 x √2
= √4 x √2 x √2
= √4 x 2
= √2x2 x 2
=√2 x √2 x 2
=2 x 2
Final answer equals 4//.
😊😊 I hope everyone is following and understanding it. I drop a comment if you don't I would explain.

Let's move to the DIVISION OF SURDS.
1. √9/7
= √9 ÷ √7
= √3 x √3 / √7
= 3/√7
.. That's the final answer.. Nothing to simplify anymore so we stop there.
2. √4/5
= √2 x √2 / √5
= 2/√5
Nothing to simplify anymore.. That's the final answer.

 Now Another part of Surd is RATIONALIZING THE DENOMINATOR.. To rationalise means Of a number, capable of being expressed as the ratio of two integers.
¾ is a rational number, but √2 is an irrational number. And Denominator is the number or expression written below the line in a fraction (thus 2 in ½)... Examples now 👇
1. 21/√7
= 21 x √7 / √7 x√7
= 21√7 / 7 ( denominator with same root so we apply rule of Surd)
Final answer equals = 3√7. (numerator 21,divided by denominator 7).

2. 10/√5 = 10 x √5 / √5 x √5
= 10√5 / 5
= 2√5..

 MULTIPLICATION OF SURDS INVOLVING BRACKETS.
1. [3√5 + 2] [√5 + 3]
= [3√5 x √5] + [3√5 x 3] + [2x√5 + 2x3] (after collecting like terms)
= [3√25 + 3x3√5 + 2√5+6]
= [3√25 + 9√5 + 2√5+6]
= [3x5 + 9√5 + 2√5+6]
= [15 + 9+2 + √5x√5 + 6]
= [15 +11√5 +6]
= 15+6 + 11√5
= 21 +11√5. (final answer).

 I HOPE Y'ALL UNDERSTAND IT.. KEEP PRACTICING AND DROP A COMMENT IF YOU DON'T UNDERSTAND.. THANKS 😊