- 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
State, with reason, which of the following are surds and which are not:
(i) √𝟏𝟖𝟎
(ii) \sqrt[4]{27}
(iii) \sqrt[5]{128}
(iv) \sqrt[3]{64}
(v) \sqrt[3]{23}.\sqrt[3]{40}
(vi) \sqrt{-125}
(vii) √𝝅
(viii) √𝟑 + √𝟐
(i) \sqrt{180}=\sqrt{2 \times 2 \times 5 \times 3 \times 3}=6 \sqrt{5}
Which is irrational.
∴, √180 is a surd
(ii) \sqrt[4]{27}=\sqrt[4]{3 \times 3 \times 3}
Which is irrational.
\sqrt[4]{27} is a surd
(iii) \sqrt[5]{128}=\sqrt[5]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}=2 \sqrt[5]{4}
Which is irrational.
\sqrt[5]{128} is a surd
(iv) \sqrt[3]{64}=\sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2}=4
Which is rational.
∴, \sqrt[3]{64} is not a surd
(v) \sqrt[3]{25} \cdot \sqrt[3]{40}=\sqrt[3]{5 \times 5 \times 2 \times 2 \times 2 \times 5}=2 \times 5=10
Which is rational.
∴, \sqrt[3]{23}.\sqrt[3]{40} is not a surd
(vi) \begin{aligned} \sqrt[3]{-125} &=\sqrt[3]{-5 \times-5 \times-5} \\ &=-5 \end{aligned}
Which is rational.
∴, \sqrt{-125} is not a surd
(vii) √𝜋 is not a surd as 𝜋 is irrational.
(viii) √3 + √2 is not a surd as 3 + √2 is irrational.
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