Square of an Odd Number as a Sum

Q.

(i) Express 81 as the sum of 9 odd numbers.
(ii) Express 100 as the sum of 10 odd numbers

Q. Find the sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19, without performing each term addition.

1. 100
2. 64
3. 90
4. 81

Q.

Question 90

Solve the following question:

Express 81 as the sum of first nine consecutive odd numbers.

Q. (i) Express $49$ as sum of $7$ odd numbers
(ii) Express $121$ as sum of $11$ odd numbers.

Q. Without adding, find the sum
(i) $1+3+5+7+9$
(ii) $1+3+5+7+9+11+13+15+17+19$
(iii) $1+3+5+7+9+11+13+15+17+19+21+23$

Q. Using the given pattern, find the missing numbers:
[2 marks]
$1^2+2^2+2^2=3^2$
$2^2+3^2+6^2=7^2$
$3^2+4^2+{12}^2={13}^2$
$4^2+5^2+{\underset{–}{}}^2={21}^2$
$5^2+{\underset{–}{}}^2+{30}^2={31}^2$
$6^2+7^2+{\underset{–}{}}^2={\underset{–}{}}^2$

Q. $(125{)}^2$ is equal to the sum of one consecutive number $7813.$ Find the other.

1. $7814$
2. $7815$
3. $7816$
4. $7812$

Q. A square land has length $2\sqrt{10}$ ft. The cost of fencing the land is $ 8/ft. The final cost of fencing the land is .

1. $64
2. $\$64\sqrt{10}$
3. $\$16\sqrt{10}$
4. $\$8\sqrt{10}$

Q. Find the next two terms of the sequence: $6,2,12,4,24,...$

1. $8,48$
2. $10,60$
3. $6,36$

Q. Express $169$ as sum of two consecutive numbers.

Q.

Evaluate the expression $-5^2·4$.

Q. A square land has length $2\sqrt{10}$ ft. The cost of fencing the land is $ 8/ft. The final cost of fencing the land is .

1. $64
2. $\$64\sqrt{10}$
3. $\$16\sqrt{10}$
4. $\$8\sqrt{10}$

Q. $24+25=?$

1. $49$
2. $34$
3. $7^2$
4. $36$

Q. $5^2=?$

1. $25$
2. $15$
3. $14$
   
4. $12+13$

Q. Express the following as the sum of two consecutive integers.
${19}^2$

Q. Find the sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19, without performing each term addition.

1. 100
2. 64
3. 90
4. 81

Q. Find the sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19, without performing each term addition.

1. 100
2. 64
3. 90
4. 81

Q.

Without adding, find the sum:

1 +3 + 5+7 + 9 +11 +13+ 15 + 17+19

Q. Express the following as the sum of two consecutive integers.
${33}^2$

Q. The square of an odd number is equal to the sum of two consecutive positive numbers.

1. False
2. True

Q. $(25{)}^2$ is equal to the sum of one consecutive number 313. Find the other.

1. $312$
2. $314$
3. $315$
4. $311$

Q. Which of the following squares are square of odd number?
$4225$

Q. Find the sum of two consecutive number for $(13{)}^2$.

1. $84$ and $85$
2. $83$ and $84$
3. $86$ and $82$
4. $81$ and $80$

Q. The square of an odd number is equal to the sum of two consecutive positive numbers.

1. False
2. True

Q. The number of zeroes at the end of a perfect square is always odd.

1. True
2. False

Q. Express the following as the sum of two consecutive integers.
${47}^2$

Q. Express 49 as the sum of odd natural numbers.

Q.

The value of ${1000}^0$ is $1000$.

1. True

2. False

Q. Which of the following squares are square of odd number?
$484$

Q. Find the sum of two consecutive numbers for $(15{)}^2$.

1. 112 and 113
2. 113 and 115
3. 115 and 112
4. 113 and 114