RS Aggarwal solution class 8 chapter 3 Squares and Square roots Exercise 3G

Exercise 3G

Page-58

Q1 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 1:

Evaluate:
$\sqrt{\frac{16}{81}}$

Answer 1:

$\sqrt{\frac{16}{81}}=\frac{\sqrt{16}}{\sqrt{81}}$



∴  $\sqrt{\frac{16}{81}}=\frac{\sqrt{16}}{\sqrt{81}}=\frac{4}{9}$

Q2 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 2:

Evaluate:
$\sqrt{\frac{64}{225}}$

Answer 2:

$\sqrt{\frac{64}{225}}=\frac{\sqrt{64}}{\sqrt{225}}$

Using long division method:
$\sqrt{64}=8$




$\sqrt{225}=15$

 

$\therefore \sqrt{\frac{64}{225}}=\frac{\sqrt{64}}{\sqrt{225}}=\frac{8}{15}$

Q3 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 3:

Evaluate:
$\sqrt{\frac{121}{256}}$

Answer 3:

$\sqrt{\frac{121}{256}}=\frac{\sqrt{121}}{\sqrt{256}}$

Using division method:

$\sqrt{121}=11$






∴$\sqrt{\frac{121}{256}}=\frac{\sqrt{121}}{\sqrt{256}}=\frac{11}{16}$

Q4 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 4:

Evaluate:
$\sqrt{\frac{625}{729}}$

Answer 4:

$\sqrt{\frac{625}{729}}=\frac{\sqrt{625}}{\sqrt{729}}$

Using long division method:


$\sqrt{625}=25$



$\sqrt{729}=27$

∴$\sqrt{\frac{625}{729}}=\frac{\sqrt{625}}{\sqrt{729}}=\frac{25}{27}$

Q5 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 5:

Evaluate:
$\sqrt{3\frac{13}{36}}$

Answer 5:

$$\begin{gathered} \sqrt{3\frac{13}{36}} \\ =\sqrt{\frac{121}{36}} \\ =\frac{\sqrt{121}}{\sqrt{36}} \\ =\frac{\sqrt{11\times 11}}{\sqrt{6\times 6}} \\ =\frac{11}{6} \\ =1\frac{5}{11} \end{gathered}$$

Q6 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 6:

Evaluate:
$\sqrt{4\frac{73}{324}}$

Answer 6:

$\sqrt{4\frac{73}{324}}=\sqrt{\frac{1369}{324}}=\frac{\sqrt{1369}}{\sqrt{324}}$

Using long division method:
$\sqrt{1369}=37$



$\sqrt{324} = \sqrt{2\times 2\times 9\times 9} = 2\times 9 = 18$



∴$\sqrt{4\frac{73}{324}}=\frac{37}{18}=2\frac{1}{18}$

Q7 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 7:

Evaluate:
$\sqrt{3\frac{33}{289}}$

Answer 7:

$\sqrt{3\frac{33}{289}}=\sqrt{\frac{900}{289}}=\frac{\sqrt{900}}{\sqrt{289}}$

Using long division method:


$\sqrt{289}=17$

And

$\sqrt{900} = \sqrt{2\times 2\times 5\times 5\times 3\times 3} = 2\times 5\times 3 = 30$


∴ $\sqrt{3\frac{33}{289}}=\frac{30}{17}=1\frac{13}{17}$

Q8 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 8:

Evaluate:
$\frac{\sqrt{80}}{\sqrt{405}}$

Answer 8:

We have:

$$\begin{gathered} \frac{\sqrt{80}}{\sqrt{405}} \\ =\sqrt{\frac{80}{405}} \\ =\sqrt{\frac{16}{81}} \\ =\frac{\sqrt{16}}{\sqrt{81}} \\ =\frac{4}{9} \end{gathered}$$

Q9 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 9:

Evaluate:
$\frac{\sqrt{1183}}{\sqrt{2023}}$

Answer 9:

We have:

$$\begin{gathered} \frac{\sqrt{1183}}{\sqrt{2023}} \\ =\sqrt{\frac{1183}{2023}} \\ = \sqrt{\frac{169}{289}} \\ =\frac{\sqrt{169}}{\sqrt{289}} \\ =\frac{\sqrt{13\times 13}}{\sqrt{17\times 17}} \\ =\frac{13}{17} \end{gathered}$$

Q10 | Ex-3G | Class 8 | RS AGGARWAL | Squares and Square roots | Chapter 3 | myhelper

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Question 10:

Evaluate:
$\sqrt{98}\times \sqrt{162}$

Answer 10:

We have:

$$\begin{gathered} \sqrt{98}\times \sqrt{162} \\ =\sqrt{98\times 162} \\ =\sqrt{2\times 7\times 7\times 2\times 9\times 9} \\ =2\times 7\times 9 \\ =126 \end{gathered}$$