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4. Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in Constructing this manner, you can get the line segment Pn-1Pn by square root spiral drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3,….,Pn,… ., and joined them to create a beautiful spiral depicting √2, √3, √4, …
13
Oct
4. Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw [...]
3. Show how √5 can be represented on the number line.
13
Oct
3. Show how √5 can be represented on the number line. 3. Show how √5 can be represented on the number line. October 13, 2020 Category: Chapter 1 - Number Systems , Maths , NCERT Class 9 ,
2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
13
Oct
2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number. 2. Are the square roots of all positive integers irrational? If not give an example of the square root of a number that is a rational number. October [...]
1. State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form √m, where m is a natural number. (iii) Every real number is an irrational number.
13
Oct
1. State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form √m, where m is a natural number. (iii) Every real number is an irrational number. 1. State whether the following statements are true [...]
4. State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number.
13
Oct
4. State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number. 1. Is zero a rational number? Can you write it in the form p/q where p and [...]
3. Find five rational numbers between 3/5 and 4/5.
13
Oct
3. Find five rational numbers between 3/5 and 4/5. 3. Find five rational numbers between 3/5 and 4/5. October 13, 2020 Category: Chapter 1 - Number Systems , Maths , NCERT Class 9 ,
2. Find six rational numbers between 3 and 4.
13
Oct
2. Find six rational numbers between 3 and 4. 2. Find six rational numbers between 3 and 4. October 13, 2020 Category: Chapter 1 - Number Systems , Maths , NCERT Class 9 ,
1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?
13
Oct
1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0? 1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0? October 13, 2020 Category: Chapter 1 - [...]
4. If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?
13
Oct
4. If 31z5 is a multiple of 3, where z is a digit, what might be the values of z? 4. If 31z5 is a multiple of 3 what might be the values of z? where z is a digit October 13, 2020 Category: Chapter 16 - Playing with Numbers , Maths , NCERT Class [...]
3. If 24x is a multiple of 3, where x is a digit, what is the value of x? (Since 24x is a multiple of 3, its sum of digits 6+x is a multiple of 3; so 6+x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, … . But since x is a digit, it can only be that 6+x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.)
13
Oct
3. If 24x is a multiple of 3, where x is a digit, what is the value of x? (Since 24x is a multiple of 3, its sum of digits 6+x is a multiple of 3; so 6+x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, … . But since x [...]
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-12 ,
… . But since x is a digit ,
15 ,
18 ,
3. If 24x is a multiple of 3 ,
3% ,
6 ,
9 ,
it can only be that 6+x = 6 or 9 or 12 or 15. Therefore ,
its sum of digits 6+x is a multiple of 3; so 6+x is one of these numbers: 0 ,
what is the value of x? (Since 24x is a multiple of 3 ,
where x is a digit ,
x = 0 or 3 or 6 or 9. Thus ,
x can have any of four different values.) ,