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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?

Solution:

(1) \(\frac { 5 }{ 64 }\)

Hint:

\(\frac { 5 }{ 64 }\) = \(\frac{5}{2^{6}}\)

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:

2^{2} = 4 and 2.5^{2} = 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 × \(0.\overline { 142857 }\) = \(0.\overline { 714285 }\)

Question 9.

Find the odd one out of the following.

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

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

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\(\sqrt{10}\)

Question 18.

(0.000729)^{\(\frac{-3}{4}\) ×} (0.09)^{\(\frac{-3}{4}\)} = ____.

Solution:

(4) \(\frac{10^{6}}{3^{6}}\)

Hint :

Question 19.

If \( \sqrt{9^{x}}=\sqrt[3]{9^{2}}\) , than x = ___

Solution:

(2) \(\frac { 4 }{ 3 }\)

Hint:

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 × 10^{1} m^{2}

(2) 9 × 10^{9} m^{2}

(3) 2 × 10^{10} m^{2}

(4) 20 × 10^{20} m^{2}

Solution:

(3) 2 × 10^{10} m^{2
}Hint:

l = 5 × 10^{5} metres; b = 4 × 10^{4} metres

∴ Area = l × b = 5 x 10^{5} × 4 × 10^{4}

= 20 × 10^{5+4}= 20 × 10^{9}= 2.0 × 10^{1} × 10^{9} = 2 × 10^{10}m^{2}