Classify the following numbers as rational or irrational :
(i) \(\sqrt23 \)
(ii) \(\sqrt225 \)
(iii) 0.3796
(iv) 7.478478...
(v) 1.101001000100001...
Classify the following numbers as rational or irrational:
(i) \(2 - \sqrt5\)
(ii) \((3 + \sqrt23) - \sqrt23\)
(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}\)
(iv) \(\frac{1}{\sqrt{2}}\)
(v) 2π
Write the degree of each of the following polynomials:
(i) 5x 3 + 4x 2 + 7x (ii) 4 – y 2 (iii) 5t – √7 (iv) 3.
Simplify each of the following expressions:
(i) (3 + √3)(2 + √2)
(ii) (3 + √3)(3 - √3)
(iii) (√5 + √2 )2
(iv) (√5 - √2)(√5 + √2)
Classify the following as linear, quadratic and cubic polynomials:
(i) x 2 + x (ii) x – x 3 (iii) y + y 2 + 4 (iv) 1 + x (v) 3t (vi) r 2 (vii) 7x 3
31.8
25.4
12.4
4.3
4.1
22.0
(i) Represent the information given above graphically. (ii) Which condition is the major cause of women’s ill health and death worldwide? (iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.
Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5 (ii) p(x) = x – 5 (iii) p(x) = 2x + 5 (iv) p(x) = 3x – 2 (v) p(x) = 3x
(vi) p(x) = ax, a ≠ 0 (vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.
Rationalise the denominators of the following:
(i) \(\frac{1 }{ \sqrt{7 }}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)