Question 11 Mark
Find the number of digits in the square root of $390625$ (without any calculation).
AnswerNumber $(n)$ of digits in $390625 = 6$ which is even.
$\therefore$ Number of digits in the square root of $390625 = \frac{n}{2} = \frac{6}{2} = 3$
View full question & answer→Question 21 Mark
Find the number of digits in the square root of $27225$ (without any calculation).
AnswerNumber $(n)$ of digits in $27225 = 5$ which is odd.
$\therefore $ Number of digits in the square root of $27225 = \frac{{n + 1}}{2} = \frac{{5 + 1}}{2} = \frac{6}{2} = 3$
View full question & answer→Question 31 Mark
Find the number of digits in the square root of $4489$ (without any calculation).
AnswerNumber $(n)$ of digits in $4489 = 4$ which is even.
$\therefore $ Number of digits in the square root of 4$489 = \frac{n}{2} = \frac{4}{2} = 2$
View full question & answer→Question 41 Mark
Find the number of digits in the square root of $144$ (without any calculation).
AnswerNumber $(n)$ of digits in $144 = 3$ which is odd.
$\therefore $ Number of digits in the square root of $144 = \frac{{n + 1}}{2} = \frac{{3 + 1}}{2} = \frac{4}{2} = 2$
View full question & answer→Question 51 Mark
Find the number of digits in the square root of $64$ (without any calculation).
AnswerNumber $(n)$ of digits in $64 = 2$ which is even.
$\therefore $ Number of digits in the square root of $64 = \frac{n}{2} = \frac{n}{2} = 1$
View full question & answer→Question 61 Mark
Without any calculation, find whether $441$ is a perfect square.
AnswerThe number may be a perfect square as the square numbers end with $0, 1, 4, 5, 6$ or $9.$
Given number $441$ has its digit $1.$ So it would be a perfect square number.
View full question & answer→Question 71 Mark
Without any calculation, find whether $408$ is a perfect square.
AnswerThe number $408$ is not a perfect square because it ends in $8$ whereas the square numbers end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 81 Mark
Without any calculation, find whether $257$ is a perfect square.
AnswerThe number $257$ is not a perfect square because it ends in $7$ whereas the square numbers end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 91 Mark
Without any calculation, find whether $153$ is a perfect square or not.
AnswerThe number $153$ is not a perfect square because it ends in $3$ whereas the square numbers end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 101 Mark
What could be the possible 'one's' digits of the square root of $657666025.$
AnswerThe units digit of the square root of the number $657666025$ could be $5.$
View full question & answer→Question 111 Mark
What could be the possible 'one's' digits of the square root of $998001.$
AnswerThe units digit of the square root of the number $998001$ could be $1$ or $9.$
View full question & answer→Question 121 Mark
What could be the possible 'one's' digits of the square root of $99856.$
AnswerThe units digit of the square root of the number $99856$ could be $4$ or $6.$
View full question & answer→Question 131 Mark
What could be the possible 'one's' digits of the square root of $9801.$
AnswerThe units digit of the square root of the number $9801$ is $9.$
View full question & answer→Question 141 Mark
Express $121$ as the sum of $11$ odd numbers.
Answer$121 ( = 11^2) = 1 + 3 + 5 + 7 + 9 + 11 + 13 +15 +17 + 19 + 21.$
View full question & answer→Question 151 Mark
Express $49$ as the sum of $7$ odd numbers.
Answer$49 (= 7^2) = 1 + 3 + 5 + 7 + 9 + 11 + 13$
View full question & answer→Question 161 Mark
Without adding, find the sum: $1 + 3 + 5 + 7 + 9 + 11 +13 + 15 + 17 + 19 + 21 + 23$
AnswerAs per the question, we have to calculate the sum of first twelve odd natural numbers
Therefore, $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = 12^2= 144$
View full question & answer→Question 171 Mark
Without adding, find the sum: $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +17 + 19$
AnswerWe know that the sum of first n odd natural numbers = $n^2$
Therefore, $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19$
$= 10^2$
$= 100$
View full question & answer→Question 181 Mark
Without adding, find the sum: $1 + 3 + 5 + 7 + 9$
AnswerAs per the question, we have to find the sum of first five odd natural numbers.
Therefore, $1 + 3 + 5 + 7 + 9 = 5^2= 25$
View full question & answer→Question 191 Mark
Is the square of $82004$ will be an odd number?
Answer$82004 –$ Unit’s digit of given number is $4$ and square of $4$ is $16.$
Therefore, the square of $82004$ would not be an odd number.
View full question & answer→Question 201 Mark
Is the square of $7779$ will be an odd number?
AnswerBecause $7779$ is an odd number, therefore its square will be an odd number.
View full question & answer→Question 211 Mark
Is the square of $2826$ will be an odd number?
AnswerBecause $2826$ is an even number, therefore its square will not be an odd number.
View full question & answer→Question 221 Mark
Is the square of $431$ will be an odd number?
Answer$\therefore$ $431$ is an odd number
$\therefore $ Its square will also be an odd number.
View full question & answer→Question 231 Mark
The number $505050$ is obviously not a perfect square. Give reason.
AnswerThe number $505050$ is not a square number because the number of zeroes at the end of a square number ending with zero is always even.
View full question & answer→Question 241 Mark
The number $222000$ is obviously not perfect square. Give reason.
Answer$222000$. The number $222000$ is not a square number because the number of zeroes at end of a square number ending with zeros is always even.
View full question & answer→Question 251 Mark
The number $89722$ is obviously not a perfect square. Give a reason.
AnswerThe number $89722$ is not a square number because it ends in $2$ whereas the square numbers end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 261 Mark
The number $64000$ is obviously not perfect square. Give reason.
Answer$64000$. The number $64000$ is not a square number because the number of zero at the end of a square numbers ending with zeroes is always even.
View full question & answer→Question 271 Mark
The number $222222$ is obviously not a perfect square. Give reason.
Answer$222222$. The number $222222$ is not a perfect square because it ends with $2$ whereas the square numbers end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 281 Mark
The number $7928$ is obviously not perfect square. Give a reason?
AnswerThe number $7928$ is not a perfect square because it ends with $8$ whereas the square numbers end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 291 Mark
The number $23453$ is obviously not a perfect square. Give a reason.
AnswerThe number $23453$ is not a perfect square because it ends with $3$ whereas the square of a number end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 301 Mark
The number $1057$ is obviously not perfect square. Give reason.
Answer$1057$. The number $1057$ is not a perfect square because it ends with $7$ whereas the square numbers end with $0, 1, 4, 5, 6$ or $9.$
View full question & answer→Question 311 Mark
What will be the unit digit of the square of $12796?$
AnswerThe unit digit of the square of the number $12796$ will be $6.$
View full question & answer→Question 321 Mark
What will be the unit digit of the square of $99880?$
AnswerThe unit digit of the square of the number $99880$ will be $0.$
View full question & answer→Question 331 Mark
What will be the unit digit of the square of $52698?$
AnswerThe unit digit of the square of the number $52698$ will be $4.$
View full question & answer→Question 341 Mark
What will be the unit digit of the square of $26387?$
AnswerThe unit digit of the square of the number $26387$ will be $9.$
View full question & answer→Question 351 Mark
What will be the unit digit of the square of $1234?$
AnswerThe unit digit of the square of the number $1234$ will be $6.$
View full question & answer→Question 361 Mark
What will be the unit digit of the square of $3853?$
AnswerThe unit digit of the square of the number $3853$ will be $9.$
View full question & answer→Question 371 Mark
What will be the unit digit of the square of $799?$
AnswerThe number $799$ contains its unit’s place digit $9.$ So, square of $9$ is $81$. Hence, unit’s digit of square of $799$ is $1.$
View full question & answer→Question 381 Mark
What will be the unit digit of the square of $272?$
AnswerThe unit digit of the square of the number $272$ will be $4.$
View full question & answer→Question 391 Mark
What will be the unit digit of the square of $55555?$
AnswerThe unit digit of the square of the number $55555$ will be $5.$
View full question & answer→Question 401 Mark
What will be the unit digit of the square of $81?$
AnswerThe unit digit of the square of the number $81$ will be $1.$
View full question & answer→