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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.9

Multiple Choice Questions :
Question 1.
If n is a natural number then \(\sqrt{n}\) is
(1) always a natural number
(2) always an irrational number
(3) always a rational number
(4) may be rational or irrational
Solution:
(4) may be rational or irrational

Question 2.
Which of the following is not true?
(1) Every rational number is a real number.
(2) Every integer is a rational number.
(3) Every real number is an irrational number.
(4) Every natural number is a whole number.
Solution:
(3) Every real number is an irrational number
Hint:
Real numbers contain rationals and irrationals.

Question 3.
Which one of the following, regarding sum of two irrational numbers, is true?
(1) always an irrational number
(2) may be a rational or irrational number.
(3) always a rational number
(4) always an integer.
Solution:
(2) may be a rational or irrational number

Question 4.
Which one of the following has a terminating decimal expansion?
Samacheer Kalvi 9th Maths Chapter 2 Real Numbers Ex 2.9 1
Solution:
(1) \(\frac { 5 }{ 64 }\)
Hint:
\(\frac { 5 }{ 64 }\) = \(\frac{5}{2^{6}}\)

Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.9

Question 5.
Which one of the following is an irrational number?
(1) \(\sqrt { 25 }\)
(2) \(\sqrt { \frac { 9 }{ 4 } }\)
(3) \(\frac { 7 }{ 11 }\)
(4) π
Solution:
(4) π
Hint:
π represents a irrational number

Question 6.
An irrational number between 2 and 2.5 is
(1) \(\sqrt { 11 }\)
(2) \(\sqrt { 5 }\)
(3) \(\sqrt { 2.5 }\)
(4) \(\sqrt { 8 }\)
Solution:
(2) \(\sqrt { 5 }\)
Hint:
22 = 4 and 2.52 = 6.25

Question 7.
The smallest rational number by which – should be multiplied so that its decimal expansion terminates after one place of decimal is
(1) \(\frac { 1 }{ 10 }\)
(2) \(\frac { 3 }{ 10 }\)
(3) 3
(4) 30
Solution:
(2) \(\frac { 3 }{ 10 }\)
Hint:
\(\frac { 3 }{ 10 }\) is the small number.

Question 8.
If \(\frac { 1 }{ 7 }\) = \(0.\overline { 142857 }\) then the value of \(\frac { 5 }{ 7 }\) is
(1) \(0.\overline { 142857 }\)
(2) \(0.\overline { 714285 }\)
(3) \(1.\overline { 571428 }\)
(4) 0.714285
Solution:
(2) \(0.\overline { 714285 }\)
Hint:
5 × \(\frac { 1 }{ 7 }\) = 5 × \(0.\overline { 142857 }\) = \(0.\overline { 714285 }\)

Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.9

Question 9.
Find the odd one out of the following.
Samacheer Kalvi 9th Maths Chapter 2 Real Numbers Ex 2.9 2
Solution:
(4) \(\frac{\sqrt{54}}{\sqrt{18}}\)
Hint:
\(\sqrt { 72 }\) × \(\sqrt { 8 }\) = \(\sqrt { 9\times8 }\) × \(\sqrt { 8 }\) = 3 × 8 = 24

Question 10.
\(0.\overline { 34 }\) + \(0.3\overline { 4 }\) =
(1) \(0.6\overline { 87 }\)
(2) \(0.\overline { 68 }\)
(3) \(0.6\overline { 8 }\)
(4) \(0.68\overline { 7 }\)
Solution:
(1) \(0.6\overline { 87 }\)
Hint:
0.343434 … + 0.344444 … = \(0.6\overline { 87 }\)

Question 11.
Which of the following statement is false?
(1) The square root of 25 is 5 or -5
(2) \(\sqrt { 25 }\) = 5
(3) –\(\sqrt { 25 }\) = -5
(4) \(\sqrt { 25 }\)= ±5
Solution:
(4) \(\sqrt { 25 }\) = ±5

Question 12.
Which one of the following is not a rational number?
(1) \(\sqrt { \frac { 8 }{ 18 } }\)
(2) \(\frac { 7 }{ 3 }\)
(3) \(\sqrt { 0.01 }\)
(4) \(\sqrt { 13 }\)
Solution:
(4) \(\sqrt { 13 }\)
Hint:
(1) \(\sqrt { \frac { 8 }{ 18 } }\) = \(\sqrt { \frac { 4 }{ 9 } }\) = \(\frac { 2 }{ 3 }\) is a arational number
(2) \(\frac { 7 }{ 3 }\) is a rational number
(3) \(\sqrt { 0.01 }\) = \(\sqrt { \frac { 1 }{ 100 } }\) = \(\frac { 2 }{ 3 }\) is a rational number
(4) \(\sqrt { 13 }\) is a rational number

Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.9

Question 13.
\(\sqrt { 27 }\) + \(\sqrt { 12 }\) =
(1) \(\sqrt { 39 }\)
(2) \(5\sqrt { 6 }\)
(3) \(5\sqrt { 3 }\)
(4) \(3\sqrt { 5 }\)
Solution:
(3) \(5\sqrt { 3 }\)
Hint:
\(\sqrt { 27 }\) + \(\sqrt { 12 }\) = \(\sqrt{9 \times 3}+\sqrt{4 \times 3}=3 \sqrt{3}+2 \sqrt{3}=5 \sqrt{3}\)

Question 14.
if \(\sqrt { 80 }\) = k\(\sqrt { 5 }\), then k =
(1) 2
(2) 4
(3) 8
(4) 16
Solution:
(2) 4
Hint: \(\sqrt { 80 }\) = \(\sqrt{16 \times 5}=4 \sqrt{5}=k \sqrt{5}\) ⇒ k = 4

Question 15.
\(4 \sqrt{7} \times 2 \sqrt{3}\) =
(1) 6\(\sqrt{10}\)
(2) 8\(\sqrt{21}\)
(3) 8\(\sqrt{10}\)
(4) 6\(\sqrt{21}\)
Solution:
(2) 8\(\sqrt{21}\)
Hint:
\(4 \sqrt{7} \times 2 \sqrt{3}\) = \(8\times\sqrt{7 \times 3}\) = 8\(\sqrt{21}\)

Question 16.
When written with a rational denominator, the expression \(\frac{2 \sqrt{3}}{3 \sqrt{2}}\) can be simplified as
Samacheer Kalvi 9th Maths Chapter 2 Real Numbers Ex 2.9 3
Solution:
(3) \(\frac{\sqrt{6}}{3}\)
Hint:
\(\frac{2 \sqrt{3}}{3 \sqrt{2}}=\frac{2 \sqrt{3}}{3 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{2 \sqrt{6}}{3 \times 2}=\frac{2 \sqrt{6}}{63}\)

Question 17.
When (2\(\sqrt{5}\) – \(\sqrt{2}\))2 is simplified, we get
(1) 4\(\sqrt{5}\) + 2\(\sqrt{2}\)
(2) 22 – 4\(\sqrt{10}\)
(3) 8 – 4\(\sqrt{10}\)
(4) 2\(\sqrt{10}\) – 2
Solution:
(2) 22 – 4\(\sqrt{10}\)
Hint:
(2\(\sqrt{5}\) – \(\sqrt{2}\))2 = (2\(\sqrt{5}\))2 – 2 × 2\(\sqrt{5}\) × \(\sqrt{2}\) + \(\sqrt{2^{2}}\)
= 4 × 5 – 4\(\sqrt{10}\) + 2 = 22 – 4\(\sqrt{10}\)

Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.9

Question 18.
(0.000729)\(\frac{-3}{4}\) × (0.09)\(\frac{-3}{4}\) = ____.
Samacheer Kalvi 9th Maths Chapter 2 Real Numbers Ex 2.9 4
Solution:
(4) \(\frac{10^{6}}{3^{6}}\)
Hint :
Samacheer Kalvi 9th Maths Chapter 2 Real Numbers Ex 2.9 5

Question 19.
If \( \sqrt{9^{x}}=\sqrt[3]{9^{2}}\) , than x = ___
Samacheer Kalvi 9th Maths Chapter 2 Real Numbers Ex 2.9 6
Solution:
(2) \(\frac { 4 }{ 3 }\)
Hint:
Samacheer Kalvi 9th Maths Chapter 2 Real Numbers Ex 2.9 7

Question 20.
The length and breadth of a rectangular plot are 5 x 105 and 4 x 104 metres respectively. Its area is .
(1) 9 × 101 m2
(2) 9 × 109 m2
(3) 2 × 1010 m2
(4) 20 × 1020 m2
Solution:
(3) 2 × 1010 m2
Hint:
l = 5 × 105 metres; b = 4 × 104 metres
∴ Area = l × b = 5 x 105 × 4 × 104
= 20 × 105+4= 20 × 109= 2.0 × 101 × 109 = 2 × 1010m2

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