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.