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

Exercise 3D

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

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Question 1:

Find the square root of number by using the method of prime factorisation:
225

Answer 1:

By prime factorisation method:

$$\begin{gathered} 225=3\times 3\times 5\times 5 \\ \sqrt{225}=3\times 5=15 \end{gathered}$$

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

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Question 2:

Find the square root of number by using the method of prime factorisation:
441

Answer 2:

By prime factorisation:

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

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Question 3:

Find the square root of number by using the method of prime factorisation:
729

Answer 3:

Resolving into prime factors:

$729=3\times 3\times 3\times 3\times 3\times 3$

∴ $\sqrt{729}=3\times 3\times 3=27$

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

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Question 4:

Find the square root of number by using the method of prime factorisation:
1296

Answer 4:

Resolving into prime factors:

$1296=2\times 2\times 2\times 2\times 3\times 3\times 3\times 3$

∴$\sqrt{1296}=2\times 2\times 3\times 3=36$

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

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Question 5:

Find the square root of number by using the method of prime factorisation:
2025

Answer 5:

Resolving into prime factors:

$2025=3\times 3\times 3\times 3\times 5\times 5$

∴$\sqrt{2025}=3\times 3\times 5=45$

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

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Question 6:

Find the square root of number by using the method of prime factorisation:
4096

Answer 6:

Resolving into prime factors:
$4096=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

∴ $\sqrt{4096}=2\times 2\times 2\times 2\times 2\times 2=64$

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

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Question 7:

Find the square root of number by using the method of prime factorisation:
7056

Answer 7:

Resolving into prime factors:

$7056=2\times 2\times 2\times 2\times 3\times 3\times 7\times 7$

∴$\sqrt{7056}=2\times 2\times 3\times 7=84$

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

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Question 8:

Find the square root of number by using the method of prime factorisation:
8100

Answer 8:

Resolving into prime factors:

$8100=2\times 2\times 3\times 3\times 3\times 3\times 5\times 5$

∴$\sqrt{8100}=2\times 3\times 3\times 5=90$

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

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Question 9:

Find the square root of number by using the method of prime factorisation:
9216

Answer 9:

Resolving into prime factors:

$9216=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$

∴ $\sqrt{9216}=2\times 2\times 2\times 2\times 2\times 3=96$

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

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Question 10:

Find the square root of number by using the method of prime factorisation:
11025

Answer 10:

Resolving into prime factors:

$11025=3\times 3\times 5\times 5\times 7\times 7$

∴$\sqrt{11025}=3\times 5\times 7=105$

Q11 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 11:

Find the square root of number by using the method of prime factorisation:
15876

Answer 11:

Resolving into prime factors:

$15876=2\times 2\times 3\times 3\times 3\times 3\times 7\times 7$

∴$\sqrt{15876}=2\times 3\times 3\times 7=126$

Q12 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 12:

Find the square root of number by using the method of prime factorisation:
17424

Answer 12:

Resolving into prime factors:

$17424=2\times 2\times 2\times 2\times 3\times 3\times 11\times 11$

∴ $\sqrt{17424}=2\times 2\times 3\times 11=132$

Q13 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 13:

Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

Answer 13:

Resolving into prime factors:



Thus, the given number must be multiplied by 7 to get a perfect square.

New number = $252\times 7=1764$

∴$\sqrt{1764}=2\times 3\times 7=42$

Q14 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 14:

Find the smallest number by which 2925 must be divided to obtain a perfect square. Also, find the square root of the perfect square so obtained.

Answer 14:

Resolving into prime factors:

$2925=3\times 3\times 5\times 5\times 13$

13 is the smallest number by which the given number must be divided to make it a perfect square.

New number = $2925÷13=225$

$\sqrt{225}=3\times 5=15$

Q15 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 15:

1225 Plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

Answer 15:

Let the number of rows be x.
Therefore, the number of plants in each row is also x.
Total number of plants $=\left(x \times x\right)=x^2=1225$
$$\begin{gathered} x^2=1225=5\times 5\times 7\times 7 \\ x=\sqrt{1225}=5\times 7=35 \end{gathered}$$

Thus, the number of rows is 35 and the number of plants in each row is 35.

Q16 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 16:

The students of a class arranged a picnic. Each student contributed as many rupees as the number of students in the class. If the total contribution is Rs 1156, find the strength of the class.

Answer 16:

Let the number of students be $x$.
Hence, the amount contributed by each student is Rs x.

Total amount contributed $=x\times x=x^2=1156$

$$\begin{gathered} 1156=2\times 2\times 17\times 17 \\ x=\sqrt{1156}=2\times 17=34 \end{gathered}$$

Thus, the strength of the class is 34.

Q17 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 17:

Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20.

Answer 17:

The smallest number divisible by each of these numbers is their L.C.M.
L.C.M. of 6, 9, 15, 20 = 180

Resolving into prime factors: 
$180=2\times 2\times 3\times 3\times 5$
To make it a perfect square, we multiply it with 5.

Required number = $180\times 5=900$

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Q18 | Ex-3D | Squares and Square roots | Chapter 3 | Class 8 | RS AGGARWAL | myhelper

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Question 18:

Find the least square number which is exactly divisible by each of the numbers 8, 12, 15 and 20.

Answer 18:

The smallest number divisible by each of these numbers is their L.C.M.
L.C.M. of 8, 12, 15, 20 = 120

Resolving into prime factors: 
$120=2\times 2\times 2\times 3\times 5$

To make this into a perfect square, we need to multiply the number with $2\times 3\times 5=30$.

Required number = $120\times 30=3600$