Mathematics for SHS 1: Short Notes on Surds – Download PDF
Have you been struggling to understand this concept of mathematics? Kindly make some time to comb through the lines below. Follow every line and you will appreciate the value contained herein.
These short notes take you through step by step method for you to understand the concept of surds.
Surds are a fundamental concept in mathematics, and they involve irrational numbers written in a specific form. An irrational number is a number that cannot be expressed as a simple fraction (ratio) of two integers and has a non-repeating, non-terminating decimal expansion.
Some key points about surds to note
Definition
A surd is an expression containing an irrational number, usually represented as √n, where “n” is a positive integer that cannot be expressed as the exact square root of any other positive integer. For example, √2, √3, and √5 are all surds because they cannot be simplified to a whole number.
Simplifying Surds
You can simplify surds by finding the largest perfect square that divides the number under the radical sign. For example:
– √12 can be simplified to 2√3 because 12 = 4 x 3, and √4 = 2.
– √50 can be simplified to 5√2 because 50 = 25 x 2, and √25 = 5.
Operations with Surds
Addition and Subtraction
You can add or subtract surds only if they have the same irrational part.
For example, √2 + √2
= 2√2 , but you cannot simplify √2 + √3 any further.
Multiplication
To multiply surds, you can simply multiply the numbers outside the radicals and multiply the numbers inside the radicals.
For example, √2 x √3
= √(2 x 3)
= √6.
Division
To divide surds, you can divide the numbers outside the radicals and divide the numbers inside the radicals.
Find full in the PDF
Rationalizing the Denominator
Sometimes, it’s necessary to get rid of surds in the denominator of a fraction. To do this, you multiply both the numerator and denominator by a suitable expression that will eliminate the surd.
Find full in the PDF
Further examples
Example 1, Simplifying Surds
Simplify √18.
To simplify √18, we need to find the largest perfect square that divides 18. In this case, 9 is the largest perfect square that does so:
√18
= √(9 x 2)
= √9 x √2
= 3√2
√18 simplifies to 3√2.
Example 2, Surd Addition and Subtraction
Evaluate √5 + √20.
We can’t directly add these surds because they don’t have the same irrational part. However, we can simplify them first:
√5 + √20
= √5 + √(4 x 5)
= √5 + 2√5
Now that they have the same irrational part, we can add them
√5 + 2√5
= 1√5 + 2√5
= 3√5
So, √5 + √20 = 3√5.
Example 3, Surd Multiplication
Multiply √7 by √14.
To multiply these surds, simply multiply the numbers outside the radicals and the numbers inside the radicals:
√7 x √14
= √(7 x 14)
= √98
Now, let’s simplify √98:
√98
= √(49 x 2)
= √49 x √2
= 7√2
So, √7 x √14 = 7√2.
The above is just excerpts of the entire short notes, download the pdf file to access them. In the PDF, you have surds on all operations [addition, subtraction, multiplication, division] and rationalizing denominators.
Thanks for coming along, to download this file tap on the link below
Join any of the Groups
TELEGRAM HERE
JOIN WHATSAPP GROUP HERE
BECE 2024 Science Preparation Questions
Commentary and Analysis of The Weaver Bird By Kofi Awoonor
SHS General Literature: A detailed Analysis of Nightfall in Soweto by Oswald Mbuyiseni Mtshali
SHS General Literature: Nightfall In Soweto Questions – Oswald Mbuyiseni Mtshali
SHS General Literature Books: List of Literature Books for Senior High
