Mathematics Part ii Solutions Solutions for Class 7 Math Chapter 3 Square Numbers are provided here with simple step-by-step explanations. These solutions for Square Numbers are extremely popular among class 7 students for Math Square Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Part ii Solutions Book of class 7 Math Chapter 3 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Part ii Solutions Solutions. All Mathematics Part ii Solutions Solutions for class 7 Math are prepared by experts and are 100% accurate.
Page No 119:
Question 1:
Find the squares of these numbers:
(i) 
(ii)
(iii)
(iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 119:
Question 2:
Which of the numbers below are squares of fractions?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
For a number to be a square of a fraction, both the numerator and denominator of the fraction should be square numbers.
(i) The denominator of is 15, which is not the square of any number.
So, is not the square of any fraction.
(ii) The numerator of is 8, which is not the square of any number.
So, is not the square of any fraction.
(iii) The numerator and denominator of are 16 and 25, respectively, which are the squares of the numbers 4 and 5.
So, is the square of the fraction.
(iv)
The numerator and denominator of are 9 and 4, respectively, which are the squares of the numbers 3 and 2.
So, is the square of the fraction.
(v)
The numerator of is 37, which is not the square of any number.
So, is not the square of any fraction.
(vi) The numerator and denominator of are 8 and 18, respectively, which are not the squares of any numbers.
So, is not the square of any fraction.
Page No 120:
Question 1:
Find the squares of these numbers:
(i) 30
(ii) 400
(iii) 7000
(iv) 6 × 1025
Answer:
(i) Square of 30 = (30)2 = 30 × 30 = 900
(ii) Square of 400 = (400)2 = 400 × 400 = 160000
(iii) Square of 7000 = (7000)2 = 7000 × 7000 = 49000000
(iv) Square of 6 × 1025 = (6 × 1025)2 = 6 × 1025 × 6 × 1025 = 36 × 1050
Page No 120:
Question 2:
Pick out the perfect squares from these:
(i) 2500
(ii) 36000
(iii) 1500
(iv) 9 × 107
(v) 16 × 1024
Answer:
(i) 2500 = 25 × 100
= 52 × 102
= (5 × 10)2
= (50)2
So, 2500 is a perfect square.
(ii) 36000 = 36 × 1000
= 62 × 1000
Here, 1000 is not a perfect square.
So, 36000 is not a perfect square.
(iii) 1500 = 15 × 100
= 15 × 102
Here, 15 is not a perfect square. So, 1500 is not a perfect square.
(iv) 9 × 107 = (3)2 × 107
Here, the power of 107 is an odd number, whereas a square number ending with zeros should end with an even number of zeros.
So, 9 × 107 is not a perfect square.
(v) 16 × 1024 = (4)2 × (1012)2 = (4 × 1012)2
So, 16 × 1024 is a perfect square.
Page No 121:
Question 1:
Find the squares of the numbers below:
(i) 1.2
(ii) 0.12
(iii) 0.013
Answer:
(i) 1.2 =
Square of 1.2 =
(ii) 0.12 =
Square of 0.12 =
(iii) 0.013 =
Square of 0.013 =
Page No 121:
Question 2:
Which of t he numbers below can be written as a square?
(i) 2.5
(ii) 0.25
(iii) 0.0016
(iv) 14.4
(v) 1.44
Answer:
(i) 2.5 =
The denominator of is 10, which is not a perfect square.
So, the number 2.5 is not a perfect square.
(ii) 0.25 =
So, the number 0.25 is a perfect square.
(iii) 0.0016 =
So, the number 0.0016 is a perfect square.
(iv) 14.4 =
The denominator of is 10, which is not a perfect square.
So, the number 14.4 is not a perfect square.
(v) 1.44 =
So, the number 1.44 is a perfect square.
Page No 121:
Question 3:
Each number below is a square. Can you say what number it is a square of?
(i) 212
(ii) 38
(iii) 56
(iv) 134
Answer:
(i) (212) = (26)2
So, 212 is the square of 26.
(ii) (38) = (34)2
So, 38 is the square of 34.
(iii) (56) = (53)2
So, 56 is the square of 53.
(iv) (134) = (132)2
So, 134 is the square of 132.
Page No 122:
Question 1:
Using our table of squares, can’t you do these?
(i)
(ii)
(iii)
(iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 123:
Question 1:
Can you factorize these numbers and their squares as product of prime powers?
(i) 35
(ii) 45
(iii) 72
(iv) 36
(v) 49
Anything special about the exponents in the factorization of squares?
Answer:
(i) 35 = 5 × 7
Square of 35 = 352
= (5 × 7)2
= 52 × 72
(ii) 45 = 3 × 3 × 5 = 32 × 5
Square of 45 = 452
= (32 × 5)2
= 34 × 52
(iii) 72 = 2 × 2 × 2 × 3 × 3 = 23 × 32
Square of 72 = 722
= (23 × 32)2
= 26 × 34
(iv) 36 = 2 × 2 × 3 × 3 = 22 × 32
Square of 36 = 362
= (22 × 32)2
= 24 × 34
(v) 49 = 7 × 7
Square of 49 = 492
= (7 × 7)2
= 72 × 72
It can be observed from the square numbers that the exponents in the factorisation of square numbers are double the exponents in the prime factorisation of the numbers.
Page No 124:
Question 1:
Now find the square root of these numbers. (You can use our table of squares)
(i) 100
(ii) 256
(iii)
(iv)
(v) 1.44
(c) 0.01
Answer:
We know that for two numbers x and y, if x2 = y, then.
(i) 100 = 102
⇒
(ii) 256 = 162
⇒
(iii)
⇒
(iv)
⇒
(v)
⇒
(vi)
⇒
Page No 124:
Question 2:
A trick question: what is
Answer:
Page No 125:
Question 1:
Now compute the square root of these by factorization.
(i) 3025
(ii) 2304
(iii) 9604
(iv) 6561
Answer:
(i) 3025 = 5 × 5 × 11 × 11
= 52 × 112
= (5 × 11)2
= 552
We know that for two numbers x and y, if x2 = y, then.
So,
(ii) 2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
= 28 × 32
= (24)2 × 32 [since x2n = (xn)2]
= 162 × 32
= (16 × 3)2
= 482
We know that for two numbers x and y, if x2 = y, then.
So,
(iii) 9604 = 2 × 2 × 7 × 7 × 7 × 7
= 22 × 74
= 22 × (72)2 [since x2n = (xn)2]
= 22 × (49)2
= (2 × 49)2
= 982
We know that for two numbers x and y, if x2 = y, then.
So,
(iv) 6561 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3
= 38
= (34)2 [since x2n = (xn)2]
= 812
We know that for two numbers x and y, if x2 = y, then.
So,
Page No 125:
Question 2:
Next try your hand all these problems:
The perimeter of a square is 220 centimeters. Find its area.
Answer:
Given that the perimeter of the square = 220 cm.
We know that the perimeter of a square = 4 × side of the square.
⇒ 220 cm = 4 × side of the square
⇒ Side of the square = cm
= 55 cm
Now, area of the square = (side) 2
= 552 cm2
= (5 × 11)2 cm2
= 52 × 112 cm2
= 25 × 121 cm2
= 3025 cm2
Thus, the area of the square is 3025 cm2.
Page No 125:
Question 3:
Next try your hand all these problems:
The area of a square is 3136 square centimeters. What is its perimeter?
Answer:
Given that the area of the square = 3136 cm2.
We know that the area of a square = (side) 2.
⇒ 3136 cm2 = (side) 2
⇒ Side of the square = cm
Now, 3136 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7
= 26 × 72
= (23)2 × 72 [since x2n = (xn)2]
= (23 × 7)2
= (8 × 7)2
= 562
We know that for two numbers x and y, if x2 = y, then.
So,
Perimeter of a square = 4 × side of the square
= 4 × 56 cm
= 224 cm
Thus, the perimeter of the square is 224 cm.
Page No 125:
Question 4:
Next try your hand all these problems:
De Morgan was a mathematician who lived in the nineteenth country. He once said, “In the year x2 my age was x.” In which year was De Morgan born?
Answer:
We know that the 19th century starts from 1800 and ends in 1899 and that there is only one perfect square number between 1800 and 1899, which is 1849.
It is given that the age of De Morgan in the year x2, i.e., 1849, was x years.
∴ x2 = 1849
We know that for two numbers x and y, if x2 = y, then.
⇒
Now, 1849 = 43 × 43 = 432
⇒
⇒ x = 43
So, the age of De Morgan was 43 years in 1849.
Therefore, the year De Morgan was born = 1849 − 43 = 1806.
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