 # 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{27}

(iii) \sqrt{128}

(iv) \sqrt{64}

(v) \sqrt{23}.\sqrt{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{27}=\sqrt{3 \times 3 \times 3}

Which is irrational.

\sqrt{27} is a surd

(iii) \sqrt{128}=\sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}=2 \sqrt{4}

Which is irrational.

\sqrt{128} is a surd

(iv) \sqrt{64}=\sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2}=4

Which is rational.

∴, \sqrt{64} is not a surd

(v) \sqrt{25} \cdot \sqrt{40}=\sqrt{5 \times 5 \times 2 \times 2 \times 2 \times 5}=2 \times 5=10

Which is rational.

∴, \sqrt{23}.\sqrt{40} is not a surd

(vi) \begin{aligned} \sqrt{-125} &=\sqrt{-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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