CBSE Maths for Class 10th Irrational Numbers from Real Numbers

Irrational Numbers

Theorem 4

Prove that √11 is irrational.

Proof:-let √11 be rational and let its simplest form a/b.

Then a and b are integers having no common factor other than 1 and b is not equal 0

√11=a/b

11=a²/b² on squaring both sides

11b²=a²

11 divide a²

11 divide b²

11 divide a

11 is prime and 11 divides a²

Let a =11c for some positive integer c

Putting a=11c in, we get

11b²=121c²

b²=11c²

11 divide b²

11 divide b

Thus 11 is a common factor of a and b.

Know more...

Comments

Lessons-Worksheets-Question Papers-CBSE Class 2 English

Lessons-Worksheets-Question Papers-CBSE Class 2 English CBSE 2nd Class English – One and Many In this blog, we share the spelling rules used in the concept of One and Many. When there is only one of a naming word (noun), it is said to be a singular noun . When a noun shows more than one, it is said to be in the plural . We can add –S, -es, -ves or ies to show that there is more than one noun. For example, we say many birds, four biscuits, six brushes. But for the students of Class 2 , it’s very difficult and confusing to understand where to use s , es, ves or ies in the form of many. Don’t worry, it looks difficult, but it is very easy as in grammar each concept has a set of rules that need to practice. Noun ending with –s, -x, -o, -sh, -ch, and –ss form plurals by taking –es. Look at these pairs of words: Bus – Buses Brush – Brushes Continue ..... Click here ...

Magnetic and non-magnetic material Class 6 Science

Magnetic and non-magnetic material Class 6 Science A magnet is a substance that is drawn to certain magnetic materials like iron, cobalt, and nickel. Magnets have the ability to draw iron to them. Natural magnets are rocks that naturally draw iron. Non-magnetic materials include things like wood, rubber, coins, feathers, leather, etc. that are not drawn to iron. Magnet characteristics It pulls magnetic materials, such as iron. The magnet's two ends are referred to as its poles. The magnet's diametrically opposed poles are drawn together. Heating, hammering, or dropping causes it to lose its characteristics. On the basis of properties types of Magnets Temporary magnets are those magnets that are magnetic for only a little duration. Typically, iron, cobalt, or nickel are used to make them. When they are close to the powerful magnet, they act like a magnet. When they are yanked away from the powerful magnet, they stop being magnetic. Permanent magnets are magnets that have magne...

Class 3 English Practice Grammar Worksheet -The Adverb

Class 3 English Practice Grammar Worksheet -The Adverb Class 3 English – The Adverb – Kinds of Adverb Fill in the blanks with suitable Adverbs of place. Choose from the box. Up outside everywhere back down away here there ...

Takshila Learning - Online Tutorials

Search This Blog