- Chapter 1- Rational and Irrational Numbers
- Chapter 2- Compound Interest [Without Using Formula
- Chapter 3- Compound Interest [Using Formula
- Chapter 4- Expansions
- Chapter 5- Factorisation
- Chapter 6- Simultaneous Equations
- Chapter 7- Indices [exponents]
- Chapter 8- Logarithms
- Chapter 9- Triangles [Congruency in Triangles]
- Chapter 10- Isosceles Triangle
- Chapter 11- Inequalities
- Chapter 12- Mid-Point and Its Converse
- Chapter 13- Pythagoras Theorem
- Chapter 14- Rectilinear Figures
- Chapter 15- Construction of Polygons
- Chapter 16- Area Theorems
- Chapter 17- Circles
- Chapter 18- Statistics
- Chapter 19- Mean and Median
- Chapter 20- Area and Perimeter of Plane Figures
- Chapter 21- Solids
- Chapter 22- Trigonometrical Ratios
- Chapter 23- Trigonometrical Ratios of Standard Angles
- Chapter 24- Solution Of Right Triangles
- Chapter 25- Complementary angles
- Chapter 26- Co-ordinate Geometry
- Chapter 27- Graphical Solution
- Chapter 28- Distance Formula
Selina Solutions Class 9 Mathematics Solutions for Exercise 1(C) in Chapter 1 - Chapter 1- Rational and Irrational Numbers
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Write the lowest rationalizing factor of:
(i) 𝟓√𝟐
(ii) √𝟐𝟒
(iii) √𝟓 − 𝟑
(iv) 𝟕 − √𝟕
(v) √𝟏𝟖 − √𝟓𝟎
(vi) √𝟓 − √𝟐
(vii) √𝟏𝟑 + 𝟑
(viii) 𝟏𝟓 − 𝟑√𝟐
(ix) 𝟑√𝟐 + 𝟐√𝟑
(i) 5 \sqrt{2} \times \sqrt{2}=5 \times 2=10which is rational lowest rationalizing factor is \sqrt{2}
(ii) \sqrt{24}=\sqrt{2 \times 2 \times 2 \times 3}=2 \sqrt{6} lowest rationalizing factor is\sqrt{6}
(iii) (\sqrt{5}-3)(\sqrt{5}+3)=(\sqrt{5})^{2}-(3)^{2}=5-9=-4 lowest rationalizing factor is(\sqrt{5}+3)
(iv) (7-\sqrt{7})(7+\sqrt{7})=49-7=42 lowest rationalizing factor is (7+)\sqrt{7}
(v) \begin{array}{l} \sqrt{18}-\sqrt{50} \\ \begin{aligned} \sqrt{18}-\sqrt{50} &=\sqrt{2 \times 3 \times 3}-\sqrt{5 \times 5 \times 2} \\ =& 3 \sqrt{2}-5 \sqrt{2}=-2 \sqrt{2} \end{aligned} \end{array} lowest rationalizing factor is\sqrt{2}
(vi) (\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})=(\sqrt{5})^{2}-(\sqrt{2})^{2}=3 lowest rationalizing factor is \sqrt{5}+\sqrt{2}
(vii) (\sqrt{13}+3)(\sqrt{13}-3)=(\sqrt{13})^{2}-3^{2}=13-9=4 lowest rationalizing factor is \sqrt{13}-3
(viii) \begin{aligned} &\begin{aligned} 15-3 \sqrt{2} &=3(5-\sqrt{2}) \\ 15-3 \sqrt{2} &=3(5-\sqrt{2})(5+\sqrt{2}) \\ &=3 \times\left[5^{2}-(\sqrt{2})^{2}\right] \\ &=3 \times[25-2] \\ =& 3 \times 23 \\ =& 69 \end{aligned}\\ &\text { : -lowest rationalizing factor is } \end{aligned} 5+\sqrt{2}
(ix) \begin{aligned} &\begin{aligned} 3 \sqrt{2}+2 \sqrt{3} &(3 \sqrt{2}+2 \sqrt{3})(3 \sqrt{2}-2 \sqrt{3}) \\ =&(3 \sqrt{2})^{2}-(2 \sqrt{3})^{2} \\ &=9 \times 2-4 \times 3 \\ &=18-12 \\ &=6 \end{aligned}\\ &\text { Iowest rationalizing factor is } 3 \sqrt{2}-2 \sqrt{3} \end{aligned}
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