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

Exercise 3E

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

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Question 1:

Evaluate:
$\sqrt{576}$

Answer 1:

Using the long division method:



∴ $\sqrt{576} = 24$

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

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Question 2:

Evaluate:
$\sqrt{1444}$

Answer 2:

Using the long division method:




∴ $\sqrt{1444} = 38$

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

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Question 3:

Evaluate:
$\sqrt{4489}$

Answer 3:

Using the long division method:


∴ $\sqrt{4489} = 67$

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

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Question 4:

Evaluate:
$\sqrt{6241}$

Answer 4:

Using the long division method:


∴ $\sqrt{6241} = 79$

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

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Question 5:

Evaluate:
$\sqrt{7056}$

Answer 5:

Using the long division method:




∴ $\sqrt{7056} = 84$

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Question 6:

Evaluate:
$\sqrt{9025}$

Answer 6:

Using the long division method:



∴ $\sqrt{9025} = 95$

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

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Question 7:

Evaluate:
$\sqrt{11449}$

Answer 7:

Using the long division method:



∴ $\sqrt{11449}=107$

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

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Question 8:

Evaluate:
$\sqrt{14161}$

Answer 8:

Using the long division method:

 
∴ $\sqrt{14161}=119$

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

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Question 9:

Evaluate:
$\sqrt{10404}$

Answer 9:

Using the long division method:



∴ $\sqrt{10404}=102$

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Question 10:

Evaluate:
$\sqrt{17956}$

Answer 10:

Using the long division method:


∴ $\sqrt{17956} = 134$

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Question 11:

Evaluate:
$\sqrt{19600}$

Answer 11:

Using the long division method:




∴ $\sqrt{19600}=140$

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

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Question 12:

Evaluate:
$\sqrt{92416}$

Answer 12:

Using the long division method:



∴ $\sqrt{92416}=304$

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Question 13:

Find the least number which must be subtracted from 2509 to make it a perfect square.

Answer 13:

Using the long division method:


Therefore, the number that should be subtracted from the given number to make it a perfect square is 9.

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Question 14:

Find the least number which must be subtracted from 7581 to obtain a perfect square. Find this perfect square and its square root.

Answer 14:

Using the long division method:


Therefore, the number that should be subtracted from the given number to make it a perfect square is 12.
Perfect square = 7581-12
                      = 7569

Its square root is 87.

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Question 15:

Find the least number which must be added to 6203 to obtain a perfect square. Find this perfect square and its square root.

Answer 15:

Using the long division method:


Thus, to get a perfect square greater than the given number, we take the square of the next natural number of the quotient, i.e. 78.
${79}^2=6241$
Number that should be added to the given number to make it a perfect square $$\begin{gathered} =6241-6203 \\ =38 \end{gathered}$$

The perfect square thus obtained is 6241 and its square root is 79.

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Question 16:

Find the least number which must be added to 8400 to obtain a perfect square. Find this perfect square and its square root.

Answer 16:

Using the long division method:


The next natural number that is a perfect square can be obtained by squaring the next natural number of the obtained quotient, i.e. 91.
Therefore square of (91+1) = ${92}^2=8464$
Number that should be added to the given number to make it a perfect square $=8464-8400=64$
The perfect square thus obtained is 8464 and its square root is 92.

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Question 17:

Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.

Answer 17:

Smallest number of four digits $=1000$

Using the long division method:


1000 is not a perfect square.
By the long division method, the obtained square root is between 31 and 32.
Squaring the next integer (32) will give us the next perfect square.

${32}^2=1024$

Thus, 1024 is the smallest four digit perfect square.

Also, $\sqrt{1024}=32$

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Question 18:

Find the greatest number of five digits which is a perfect square. Also find the square root of the number so obtained.

Answer 18:

Greatest number of five digits $=99999$

Using the long division method:



99999 is not a perfect square. 
According to the long division method, the obtained square root is between 316 and 317.
Squaring the smaller number, i.e. 316, will give us the perfect square that would be less than 99999.

${316}^2=99856$

99856 is the required number. 
Its square root is 316.

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Question 19:

The area of a square field is 60025 m². A man cycles along its boundary at 18 km/h. In how much time will he return to the starting point?

Answer 19:

Area of the square field $= 60025 m^2$
Length of each side of the square field $=\sqrt{60025}=245m$
Perimeter of the field $=4\times 245=980 m$

                                  
The man is cycling at a speed of 18 km/h.