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MATHEMATICS [2 Mark Question Answer]

Rational and Irrational Numbers · ICSE STD 9 (ICSE - English Medium). 63 questions.

Questions · Page 2 of 2

[2 Mark Question Answer]

Question 512 Marks
Write in ascending order $: 6\sqrt5, 7\sqrt3$ and $8\sqrt2$
Answer
$ 6 \sqrt{5}=\sqrt{6^2 \times 5}=\sqrt{180}$
$ 7 \sqrt{3}=\sqrt{7^2 \times 3}=\sqrt{147}$
$ 8 \sqrt{2}=\sqrt{8^2 \times 2}=\sqrt{128}$
and $128<147<180$
$ \therefore \sqrt{128}<\sqrt{147}<\sqrt{180}$
$ \Rightarrow 8 \sqrt{2}<7 \sqrt{3}<6 \sqrt{5}$
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Question 522 Marks
Write in ascending order : $2 \sqrt[3]{5}$ and $3 \sqrt[3]{2}$
Answer
$ 2 \sqrt[3]{5}=\sqrt[3]{2^3 \times 5}=\sqrt[3]{40}$
$ 3 \sqrt[3]{2}=\sqrt[3]{3^3 \times 2}=\sqrt[3]{54}$
and $40<54$
$\Rightarrow \sqrt[3]{40}<\sqrt[3]{54}$
$ \Rightarrow 2 \sqrt[3]{5}<3 \sqrt[3]{2}$
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Question 532 Marks
Write in ascending order $: 3\sqrt5$ and $4\sqrt3$
Answer
$ 3 \sqrt{5}=\sqrt{3^2 \times 5}=\sqrt{45}$
$,4 \sqrt{3}=\sqrt{4^2 \times 3}=\sqrt{48}$
and $45 < 48$
$ \therefore \sqrt{45} < \sqrt{48}$
$\Rightarrow 3 \sqrt{5} < 4 \sqrt{3}$
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Question 542 Marks
State, whether the following numbers is rational or not : $( 3 - \sqrt3 )^2$
Answer
$( 3 - \sqrt3 ) = 3^2 - 2 ( 3 ) ( \sqrt3 ) + ( \sqrt3 )^2$
$= 9 - 6\sqrt3 + 3$
$= 12 - 6\sqrt3$
$= 6 ( 2 - \sqrt3 )$
Irrational number.
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Question 552 Marks
State, whether the following numbers is rational or not : $( 2 + \sqrt2 )^2$
Answer
$( 2 + \sqrt2 )^2 = 2^2 + 2 ( 2 ) ( \sqrt2 ) + ( \sqrt2 )^2$
$= 4 + 4\sqrt2 + 2$
$= 6 + 4\sqrt2$
Irrational number.
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Question 562 Marks
Without doing any actual division , find which of the following rational numbers have terminating decimal representation $ : '123/250\ '$
Answer
Given number is $\frac{123}{250}$
Since $250=2 \times 5 \times 5 \times 5=2^1 \times 5^3$
i.e. $250 $ can be expressed as $2^m \times 5^n$
$\therefore \frac{123}{250}$ is convertible into the terminating decimal.
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Question 572 Marks
Without doing any actual division $, $ find which of the following rational numbers have terminating decimal representation : $\frac{61}{75}$
Answer
Given number is $\frac{61}{75}$
Since $75=3 \times 5 \times 5=3^1 \times 5^2$
i.e. $75$ cannot be expressed as $2^m \times 5^n$
$\therefore \frac{61}{75}$ is not convertible into the terminating decimal.
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Question 582 Marks
Without doing any actual division, find which of the following rational numbers have terminating decimal representation: $\frac{17}{40}$
Answer
Given number is $\frac{17}{40}$
Since $40=2 \times 2 \times 2 \times 5=2^3 \times 5^1$
I.e. $40 $ can be expressed as $2^m \times 5^n$
$\therefore \frac{17}{40}$ is convertible into the terminating decimal.
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Question 592 Marks
Without doing any actual division, find which of the following rational numbers have terminating decimal representation : $\frac{43}{50}$
Answer
Given number is $\frac{46}{50}$
Since $50=2 \times 5 \times 5=2^1 \times 5^2$
I.e.$ 50 $ can be expressed as $2^m \times 5^n$
$\therefore \frac{43}{50}$ is convertible into the terminating decimal.
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Question 602 Marks
Without doing any actual division, find which of the following rational numbers have terminating decimal representation : $\frac{32}{45}$
Answer
Given number is $\frac{32}{45}$
Since, $45=3 \times 3 \times 5=3^2 \times 5^1$
I.e. $45 $ cannot be expressed as $2^m \times 5^n$
$\therefore \frac{32}{45}$ is not convertible into the terminating decimal.
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Question 612 Marks
Without doing any actual division, find which of the following rationa numbers have terminating decimal representation : $\frac{9}{14}$
Answer
Given number is $\frac{9}{14}$
Since $14=2 \times 7=2^1 \times 7^1$
I.e. $14 $ cannot be expressed as $2^{\mathrm{m}} \times 5^{\mathrm{n}}$
$\therefore \frac{9}{14}$ is not convertible into the terminating decimal.
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Question 622 Marks
Without doing any actual division, find which of the following rationa numbers have terminating decimal representation : $\frac{23}{125}$
Answer
Given number is $\frac{23}{125}$
Since $125=5 \times 5 \times 5=5^3=2^0 \times 5^3$
I.e. $125 $ can be expressed as $2^m \times 5^n$
$\therefore \frac{23}{125}$ is convertible into the terminating decimal.
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Question 632 Marks
Without doing any actual division $, $ find which of the following rational numbers have terminating decimal representation : $\frac{7}{16}$
Answer
Given number is $\frac{7}{16}$
Since $16=2 \times 2 \times 2 \times 2=2^4=2^4 \times 5^0$
I.e. $16$ can be expressed as $2^m \times 5^n$
$\therefore \frac{7}{16}$ is convertible into the terminating decimal.
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[2 Mark Question Answer] - Page 2 - MATHEMATICS STD 9 Questions - Vidyadip