Question 11 MarkWhat can you say about the parity of a number and its square?AnswerThe square of an even number is always even, and that of an odd number is always odd.View full question & answer→
Question 21 MarkWhich of the following numbers have the digit 6 in the units place?822Answer$82^2$$82 \rightarrow$ Units digit $\rightarrow 2$$2 \times 2=4$ (ends in 4)So, $82^2$ ends in 4 .View full question & answer→
Question 31 MarkWhich of the following numbers have the digit 6 in the units place?742Answer$74^2$$74 \rightarrow$ Units digit $\rightarrow 4$$4 \times 4=16$ (ends in 6)So, $74^2$ ends in 6 .View full question & answer→
Question 41 MarkWhich of the following numbers have the digit 6 in the units place?562Answer$56^2$$56 \rightarrow$ Units digit $\rightarrow 6$$6 \times 6=36$ (ends in 6)So, $56^2$ ends in 6 .View full question & answer→
Question 51 MarkWhich of the following numbers have the digit 6 in the units place?462Answer$46^2$$46 \rightarrow$ Units digit $\rightarrow 6$$6 \times 6=36$ (ends in 6)So, $46^2$ ends in 6 .View full question & answer→
Question 61 MarkWhich of the following numbers have the digit 6 in the units place?342Answer$34^2$34 $\rightarrow$ Units digit $\rightarrow 4$$4 \times 4=16$ (ends in 6)So, $34^2$ ends in 6 .View full question & answer→
Question 71 MarkWhich of the following numbers have the digit 6 in the units place?382Answer$38^2$$38 \rightarrow$ Units digit $\rightarrow 8$$8 \times 8=64$ (ends in 4)So, $38^2$ does not end in 6 .View full question & answer→
Question 81 MarkWrite 5 numbers such that you can determine by looking at their unit digit that they are not squares.Answer478, 1072, 7543, 9047, and 1257.View full question & answer→
Question 91 MarkWhat patterns do you notice? Share your observations and make conjectures.AnswerAll perfect square numbers end with 0, 1, 4, 5, 6, or 9, and none of them end with 2, 3, 7, or 8.View full question & answer→
Question 101 MarkWhich are these five lockers?AnswerThe lockers that are toggled twice are the prime numbers, since each prime number has 1 and the number itself as factors. So, the code is 2-3-5-7-11.View full question & answer→
Question 111 MarkWrite the locker numbers that remain open.Answer10 lockers with square locker numbers, i.e, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, will remain open.View full question & answer→
Question 121 MarkFind the cube roots of these numbers : $\sqrt[3]{729}=$Answer$\sqrt[3]{729}$$\begin{array}{l}729=(3 \times 3 \times 3) \times(3 \times 3 \times 3) \\=3^3 \times 3^3 \\=(3 \times 3)^3=9^3 \\\therefore \sqrt[3]{729}=9 .\end{array}$View full question & answer→
Question 131 MarkFind the cube roots of these numbers : $\sqrt[3]{512}=$Answer$\sqrt[3]{512}$$\begin{array}{l}512=(2 \times 2 \times 2) \times(2 \times 2 \times 2) \times(2 \times 2 \times 2) \\=2^3 \times 2^3 \times 2^3 \\=(2 \times 2 \times 2)^3=8^3 \\\therefore \sqrt[3]{512}=8\end{array}$View full question & answer→
Question 141 MarkFind the cube roots of these numbers : $\sqrt[3]{64}=$Answer$\sqrt[3]{64}$$\begin{array}{l}64=(2 \times 2 \times 2) \times(2 \times 2 \times 2) \\ =2^3 \times 2^3 \\ =(2 \times 2)^3=4^3 \\ \therefore \sqrt[3]{64}=4\end{array}$View full question & answer→
Question 151 MarkCan you tell what this sum is without doing the calculation?91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107 + 109.AnswerThis series has 10 consecutive odd numbers, and their sum is $10^3=1000$.View full question & answer→
Question 161 MarkWe know that 0, 1, 4, 5, 6, 9 are the only last digits possible for squares. What are the possible last digits of cubes?AnswerThe last digits of cubes can be any digit from 0 to 9.View full question & answer→