Squares and Square Roots quiz

Which of the following cannot be a perfect square?

The square root of 1296 is:

The sum 1 + 3 + 5 + 7 + 9 is equal to:

The number of non-square numbers between 9^2 and 10^2 is:

Which of the following is a Pythagorean triplet?

The units digit of 79^2 is:

The square root of 0.49 is:

The square of an odd number is always:

The number of digits in the square root of 14641 is:

The smallest number by which 180 must be multiplied to make it a perfect square is:

Is 2352 a perfect square? If not, find the smallest number by which it must be multiplied to make it a perfect square. (2 marks)

Using (a + b)^2 or (a - b)^2, find 35^2 and 47^2. (2 marks)

Express 49 as the sum of 7 odd numbers. (2 marks)

Find the square root of 100 by repeated subtraction of odd numbers, showing the steps. (2 marks)

Explain why a perfect square can never end with the digit 2, 3, 7 or 8. (2 marks)

Without adding, find the sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19. Give a reason. (2 marks)

Find the square root of 225/441. (2 marks)

How many non-square numbers lie between 25^2 and 26^2? (2 marks)

Estimate the square root of 80 to the nearest whole number. Explain your answer. (2 marks)

Observe the pattern 11^2 = 121, 101^2 = 10201, 1001^2 = 1002001. Write the value of 100001^2. (2 marks)

Find the square root of 1764 by prime factorisation and the square root of 5776 by the long division method. (3 marks)

Find the square roots of (i) 12.25 (ii) 0.0441 (iii) 108.16. (3 marks)

The area of a square plot is 60025 m^2. Find the length of its side and its perimeter. (3 marks)

Find the greatest four-digit number and the least four-digit number that are perfect squares. Write their square roots. (3 marks)

A ladder 10 m long rests against a vertical wall and reaches a window 8 m above the ground. How far is the foot of the ladder from the wall? (3 marks)

Read the passage and answer the questions. A school has 1000 students. The sports teacher wants them to stand in a square formation for the morning drill, with as many students as possible in the square and the rest standing aside. (i) How many students can stand in the largest possible square formation? (ii) How many students will be left over? (iii) How many more students would be needed to form the next larger square? (5 marks)

Read the passage and answer the questions. A square courtyard has an area of 1764 m^2. It is to be fenced, and its floor is to be covered with square tiles of side 60 cm. (i) Find the side of the courtyard. (ii) Find the length of fencing needed. (iii) How many tiles are needed to cover the floor? (5 marks)

Read the passage and answer the questions. A mason checks that a corner of a wall is a right angle by measuring 3 m along one wall and 4 m along the other, and checking that the distance between the two marks is 5 m. (i) Show that 6 m, 8 m and 10 m would also give a right angle. (ii) Using the general form 2m, m^2 - 1, m^2 + 1, find a Pythagorean triplet in which the smallest member is 12. (iii) Why does the triplet test guarantee a right angle? (5 marks)

Read the passage and answer the questions. In a maths club, Riya noticed that 1 + 3 = 4, 1 + 3 + 5 = 9 and 1 + 3 + 5 + 7 = 16, and tried to extend the pattern. (i) Find 1 + 3 + 5 + ... + 29 without adding. (ii) How many odd numbers must be added, starting from 1, to get 400? (iii) Which odd number should be added to 1 + 3 + 5 + ... + 15 to get 81? (5 marks)

Read the passage and answer the questions. A square photo frame is to have an area of 200 cm^2. The carpenter needs to know the length of each side, but 200 is not a perfect square. (i) Between which two consecutive whole numbers does the side lie? (ii) To which of them is it closer? Give a reason. (iii) Use the long division method to find the square root of 2 correct to two decimal places, and hence write the side as 10 times this value. (5 marks)

Explain the long division method for finding square roots, showing the full working for 7921. Use the same method to find the square root of 2 correct to three decimal places. (6 marks)

Draw dot diagrams to show that the sum of two consecutive triangular numbers is a square number, for 1 + 3, 3 + 6 and 6 + 10. Also draw a dot pattern showing that 1 + 3 + 5 + 7 = 16. State three other properties of square numbers. (6 marks)

Draw a factor tree for 1008. Use it to find (i) the smallest number by which 1008 must be multiplied to get a perfect square and the square root of the product (ii) the smallest number by which 1008 must be divided to get a perfect square and the square root of the quotient. (6 marks)

Draw a right-angled triangle with squares drawn on its three sides to illustrate a Pythagorean triplet. Using the general form 2m, m^2 - 1, m^2 + 1, write the triplets for m = 4 and m = 5 and verify each. Explain why every such set is a Pythagorean triplet. (6 marks)

Using the long division method, find: (i) the square root of 5.4756 (ii) the side of a square field of area 441 m^2 (iii) the least number that must be subtracted from 4000 to get a perfect square, and the square root of that perfect square. Show the full division layout for (iii). (6 marks)