RS Aggarwal solution class 8 chapter 3 Squares and Square roots Test Paper 3

Test Paper 3

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Q1 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 1:

Evaluate $\sqrt{11236}.$

Answer 1:

Using long division method:



∴  $\sqrt{11236}=106$

Q2 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 2:

Find the greatest number of five digits which is a perfect square. What is the square root of this number?

Answer 2:

The greatest 5 digit number is 99999.


$316 < \sqrt{99999} < 317$

${316}^2=99856$ 
Thus, this is the greatest 5 digit number.

$\sqrt{99856}=316$

Q3 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 3:

Find the least number of four digits which is a perfect square. What is the square root of this number?

Answer 3:

The least number of 4 digits is 1000.



$$\begin{gathered} 31< \sqrt{100}< 32 \\ {32}^2= 1024 \end{gathered}$$

1024 is the least four digit perfect square and its square root is 32.

Q4 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 4:

Evaluate $\sqrt{0.2809}.$

Answer 4:

∴ $\sqrt{0.2809}=0.53$

Q5 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 5:

Evaluate $\sqrt{3}$ correct up to two places of decimal.

Answer 5:

Q6 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 6:

Evaluate $\frac{\sqrt{48}}{\sqrt{243}}.$

Answer 6:

$$\begin{gathered} \frac{\sqrt{48}}{\sqrt{243}} \\ =\sqrt{\frac{48}{243}} \\ =\sqrt{\frac{2\times 2\times 2\times 2\times 3}{3\times 3\times 3\times 3\times 3}} \\ =\frac{\sqrt{2\times 2\times 2\times 2}}{\sqrt{3\times 3\times 3\times 3}} \\ =\frac{2\times 2}{3\times 3} \\ =\frac{4}{9} \end{gathered}$$

Q7 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 7:

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Which of the following numbers is not a perfect square?
(a) 529
(b) 961
(c) 1024
(d) 1222

Answer 7:

(d) 1222

A number ending in 2, 3, 7 or 8 is not a perfect square.

Q8 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 8:

Mark (✓) against the correct answer
$\sqrt{2\frac{1}{4}}=?$
(a) $2\frac{1}{2}$
(b) $1\frac{1}{4}$
(c) $1\frac{1}{2}$
(d) none of these

Answer 8:

(c) $1\frac{1}{2}$


$\sqrt{2\frac{1}{4}}=\sqrt{\frac{9}{4}}=\frac{\sqrt{9}}{\sqrt{4}}=\frac{\sqrt{3\times 3}}{\sqrt{2\times 2}}=\frac{3}{2}=1\frac{1}{2}$

Q9 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 9:

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Which of the following is the square of an even number?
(a) 529
(b) 961
(c) 1764
(d) 2809

Answer 9:

(c) 1764

The square of an even number is always even.

Q10 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 10:

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What least number must be added to 521 to make it a perfect square?
(a) 3
(b) 4
(c) 5
(d) 8

Answer 10:

(d) 8

$$\begin{gathered} 521+8=529 \\ \sqrt{529}=23 \end{gathered}$$  

Q11 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 11:

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What least number must be subtracted from 178 to make it a perfect square?
(a) 6
(b) 8
(c) 9
(d) 7

Answer 11:

(c) 9

$$\begin{gathered} 178-9=169 \\ \sqrt{169}=13 \end{gathered}$$

Q12 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 12:

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$\sqrt{72}\times \sqrt{98}=?$
(a) 42
(b) 84
(c) 64
(d) 74

Answer 12:

(b) 84

$\sqrt{72}\times \sqrt{98}=\sqrt{2\times 2\times 2\times 3\times 3}\times \sqrt{2\times 7\times 7}=\sqrt{2\times 2\times 2\times 3\times 3\times 2\times 7\times 7}=2\times 2\times 3\times 7=84$

Q13 Test Paper 3 Class 8 RS AGGARWAL 3 Squares and Square roots Solution

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Question 13:

Fill in the blanks.
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 = (.........)².
(ii) $\sqrt{1681}=.........$
(iii) The smallest square number exactly divisible by 2, 4, 6 is .........
(iv) A given number is a perfect square having n digits, where n is odd. Then, its square root will have ......... digits.

Answer 13:

(i) $1+3+5+7+9+11+13=(7{)}^2$ 


(ii)

 $\sqrt{1681}=41$

(iii) The smallest square number exactly divisible by 2, 4 and 6 is 36.



(iv) A given number is a perfect square having n digits, where n is odd. then, its square root will have $\left(\frac{n+1}{2}\right)$ digits.