Question 1: Find the square of each of the following numbers:
(i) (ii)
(iii)
(iv)
(v)
(vi) of
(vii)
(viii)
Answer:
(i) Square of
(ii) Square of
(iii) Square of
(iv) Square of
(v) Square
(vi) Square of
(vii) Square of
(viii) Square of
Question 2: Using prime factorization method, find which of the following are perfect square numbers:
(i) (ii)
(iii)
(iv)
(v)
(vi)
(vii)
Note: A natural number is called a perfect square, if it is the square of some natural number
Answer:
(i) (hence perfect square)
(ii) (not a perfect square)
(iii) (hence perfect square)
(iv) (hence a perfect square)
(v) (hence perfect square)
(vi) (not a perfect square)
(vii) (hence a perfect square)
Question 3: Which of the following numbers are squares of even numbers?
Note: The Square of an even number is always an even number.
,
,
,
,
,
Answer:
(square of
)
(square of
) and
(square of
) are square of even numbers.
Question 4: Using prime factorization method, find the square root of each of the following numbers:
(i) (ii)
(iii)
(vi)
(v)
(vi)
Answer:
(i) .
, square root of
(ii) . Therefore, square root of
(iii) . Therefore, square root of
(vi) . Therefore, square root of
(v) . Therefore, square root of
(vi) . Therefore, square root of
Question 5: 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. , find the strength of the class.
Answer:
Let the number of students
Each student contributed Rupees.
Therefore or
Question 6: Find the smallest number by which be multiplied to get a perfect square number.
Answer:
. Therefore multiply by
to get a perfect square
Question 7: Find the smallest number by which be multiplied to get a perfect square number. Find the square root of the resulting number.
Answer:
. Therefore multiply by
. The square root would be
Question 8: Find the smallest number by which be multiplied to get a perfect square number.
Answer:
(i) What is the perfect square number so obtained?
.
Therefore smallest number to be multiplied to to get a perfect square is
. Perfect square number
(ii) What is the square root of the resulting number?
Square root of the resulting number is
Question 9: Find the smallest number by which be divided to get a perfect square number.
Answer:
(i) What is the perfect square number so obtained?
. Hence divide it by
. The number would be
(ii) Find the square root of this number.
Square root
Question 10: Find the smallest number by which 7776 be divided to get a perfect square number.
(i) What is the resulting number? (ii) What is the square root of the number so obtained?
Answer:
(i) What is the resulting number?
. Hence divide this by
. The number would be
(ii) What is the square root of the number so obtained?
Square root
Question 11: Find the least square number which is exactly divisible by each of the numbers and
.
Answer:
Therefore the number is
Question 12: Find the square root of each of the following by division method:
i) ii)
iii)
iv)
v)
vi)
Answer:
By the long division method, we have
i)
ii)
iii)
iv)
v)
vi)
Question 13: The area of a square field is sq. meters. Find its perimeter.
Answer:
Area = side side
meter
Perimeter side
sq. meters
Question 14: Find the least number which must be subtracted from to obtain a perfect square. Find this perfect square and its square root.
Answer:
Subtract from
to obtain a perfect square. The number would be
and the square root would be
.
Question 15: Find the least number which must be subtracted from to obtain a perfect Find this perfect square and its square root.
Answer:
Subtract from
to obtain perfect square.
Question 16: Find the least number which must be added to 6203 to obtain a perfect square. Find the perfect square and its square
Answer:
Therefore
Therefore add to
to obtain a perfect square
.
Its square root would be .
Question 17: Find the least number which must be added to 506900 to make it a perfect square. Find this perfect square and its square root.
Answer:
Therefore
Therefore add to
to make it a perfect square of
.
Question 18: Find the greatest number of six digits, which is a perfect square. Find the square root of this number.
Answer:
Subtract from
to make a perfect square. The number is
.
Question 19: Find the least number of four digits which is a perfect square.
Answer:
Therefore
Therefore add to
to get the least number of four digits which is a perfect square which is
.
Question 20: Find the least number by which must be (i) decreased (ii) increased (iii) multiplied (iv) divided to make it a perfect.
Answer:
Subtract from
to make it a perfect square.
. Therefore add
to
to make it a perfect square.
. Therefore multiply by
to make it a perfect square
Or divide it by to make it a perfect square.
The exercises of this chapter is outdated and aren’t the one one which we are studying, because other chapters are up to date and current.
Request you to update this chapter as per the current syllabus, as my exams are near and I want to study badly 😀
concepts should be the same…
But, I want the same sums, please request you to work on it.