Question 512 Marks
Find the square of $46$
Answer
View full question & answer→$46 = 40 + 6$
Therefore, $46^2= (40 + 6)^2$
$= 1600 + 240 + 240 + 36$
$= 2116$
Therefore, $46^2= (40 + 6)^2$
$= 1600 + 240 + 240 + 36$
$= 2116$
Questions · Page 2 of 2
2 Marks Questions
Question 522 Marks
Find the square of $71$
Answer
View full question & answer→$71$
$71 = 70 + 1$
Therefore, $71^2= (70 + 1)^2$
$= 4900 + 70 + 70 + 1$
$= 5041$
$71 = 70 + 1$
Therefore, $71^2= (70 + 1)^2$
$= 4900 + 70 + 70 + 1$
$= 5041$
Question 532 Marks
Find the square of $93$
Answer
View full question & answer→$93 = 90 +3$
Therefore, $93^2= (90 + 3)^2$
$= 8100 + 270 + 270 + 9$
$= 8649$
Therefore, $93^2= (90 + 3)^2$
$= 8100 + 270 + 270 + 9$
$= 8649$
Question 542 Marks
Find the square of $86$
Answer
View full question & answer→$86 = 80 +6$
Therefore, $86^2= (80 + 6)^2$
$= 6400 + 480 + 480 +36$
$= 7396$
Therefore, $86^2= (80 + 6)^2$
$= 6400 + 480 + 480 +36$
$= 7396$
Question 552 Marks
Find the square of $35$
Answer
View full question & answer→$35 = 30 + 5$
Therefore, $35^2= (30 + 5)^2$
$= 900 + 150 + 150 +25$
$= 1225$
Therefore, $35^2= (30 + 5)^2$
$= 900 + 150 + 150 +25$
$= 1225$
Question 562 Marks
Find the square of $32$
Answer
View full question & answer→$32 = 30 + 2$
Therefore, $32^2= (30 + 2)^2$
$= 900 + 2$$\times$$60 + 4$
$= 1024$
Therefore, $32^2= (30 + 2)^2$
$= 900 + 2$$\times$$60 + 4$
$= 1024$
Question 572 Marks
How many number lie between square of the $99$ and $100?$
Answer
View full question & answer→Here, $n = 99$
$\therefore $ $2n = 2$ $\times $ $99 = 198$
So, $198$ numbers lie between squares of the numbers $99$ and $100$.
$\therefore $ $2n = 2$ $\times $ $99 = 198$
So, $198$ numbers lie between squares of the numbers $99$ and $100$.
Question 582 Marks
How many number lie between square of the $25$ and $26?$
Answer
View full question & answer→Here, $n = 25$
$\therefore$ $2n = 2$$\times $$25 = 50$
So, $50$ numbers lie between squares of the numbers $25$ and $26$.
$\therefore$ $2n = 2$$\times $$25 = 50$
So, $50$ numbers lie between squares of the numbers $25$ and $26$.
Question 592 Marks
How many number lie between square of the $12$ and $13?$
Answer
View full question & answer→$12$ and $13$
Here, $n = 12$
$\therefore$ $2n = 2$ $\times$ $12 = 24$
So, $24$ numbers lie between squares of the numbers $12$ and $13$.
Here, $n = 12$
$\therefore$ $2n = 2$ $\times$ $12 = 24$
So, $24$ numbers lie between squares of the numbers $12$ and $13$.
Question 602 Marks
Using the given pattern, find the missing numbers:
$1^2+2^2+2^2=3^2 $
$ 2^2+3^2+6^2=7^2$
$ 3^2+4^2+12^2=13^2 $
$4^2+ 5^2+\_^2= 21^2$
$5^2+\_^2+ 30^2 = 31^2$
$6^2+ 7^2+\_\_\_^2=\_\_\_^2$
$1^2+2^2+2^2=3^2 $
$ 2^2+3^2+6^2=7^2$
$ 3^2+4^2+12^2=13^2 $
$4^2+ 5^2+\_^2= 21^2$
$5^2+\_^2+ 30^2 = 31^2$
$6^2+ 7^2+\_\_\_^2=\_\_\_^2$
Answer
View full question & answer→$ 4^2+5^2+20^2=21^2 $
$ 5^2+6^2+30^2=31^2 $
$ 6^2+7^2+42^2=43^2 $
$ 5^2+6^2+30^2=31^2 $
$ 6^2+7^2+42^2=43^2 $
Question 612 Marks
Observe the following pattern and find the missing numbers:
$11^2= 121$
$101^2= 10201$
$10101^2= 102030201$
$1010101^2= \_\_\_\_\_\_\_\_$
$\_\_\_\_\_\_\_\_^2 = 10203040504030201$
$11^2= 121$
$101^2= 10201$
$10101^2= 102030201$
$1010101^2= \_\_\_\_\_\_\_\_$
$\_\_\_\_\_\_\_\_^2 = 10203040504030201$
Answer
View full question & answer→$ 11^2=121 $
$ 101^2=10201 $
$ 10101^2=102030201 $
$ 1010101^2=1020304030201 $
$ 101010101^2=10203040504030201 $
$ 101^2=10201 $
$ 10101^2=102030201 $
$ 1010101^2=1020304030201 $
$ 101010101^2=10203040504030201 $
Question 622 Marks
Observe the following pattern and find the missing digits.
$11^2= 121$
$101^2= 10201$
$1001^2= 1002001$
$100001^2= 1 \_\_\_\_\_\_\_\_ 2\_\_\_\_\_\_\_\_ 1$
$10000001^2= \_\_\_\_\_\_\_\_?$
$11^2= 121$
$101^2= 10201$
$1001^2= 1002001$
$100001^2= 1 \_\_\_\_\_\_\_\_ 2\_\_\_\_\_\_\_\_ 1$
$10000001^2= \_\_\_\_\_\_\_\_?$
Answer
View full question & answer→$ 11^2=121 $
$ 101^2=10201 $
$ 1001^2=1002001 $
$ 100001^2=10000200001 $
$ 10000001^2=100000020000001 $
$ 101^2=10201 $
$ 1001^2=1002001 $
$ 100001^2=10000200001 $
$ 10000001^2=100000020000001 $
Question 632 Marks
Find the square root of $1296$.
Answer
Therefore $\sqrt{1296} = 36$
View full question & answer→Therefore $\sqrt{1296} = 36$
Question 642 Marks
Find the square root of $729$.
Answer
Therefore $\sqrt{729}$ $= 27$
View full question & answer→Therefore $\sqrt{729}$ $= 27$
Question 652 Marks
Is $90$ a perfect square?
Answer
We have $90 =$ $2 \times 3 \times 3 \times 5$
The prime factors $2$ and $5$ do not occur in pairs. Therefore, $90$ is not a perfect square.
View full question & answer→We have $90 =$ $2 \times 3 \times 3 \times 5$
The prime factors $2$ and $5$ do not occur in pairs. Therefore, $90$ is not a perfect square.
Question 662 Marks
Find the square root of $6400$
Answer
Thus factors of $6400 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5$
Therefore, $\sqrt{6400} = 2 \times 2 \times 2 \times 2 \times 5 = 80$
View full question & answer→Thus factors of $6400 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5$
Therefore, $\sqrt{6400} = 2 \times 2 \times 2 \times 2 \times 5 = 80$
Question 672 Marks
Area of a square plot is $2304$ $m^2$. Find the side of the square plot.
Answer
View full question & answer→Area of square plot $= 2304$ $m^2$
Therefore, side of the square plot = $\sqrt{2304} \;m$
Finding $\sqrt{2304}$ by long division method.
Thus, the side of the square plot is $48\ m$.
Therefore, side of the square plot = $\sqrt{2304} \;m$
Finding $\sqrt{2304}$ by long division method.
Thus, the side of the square plot is $48\ m$.
Question 682 Marks
Find the square root of $12.25$.
Answer
Therefore, $\sqrt{12.25}=3.5$
View full question & answer→Therefore, $\sqrt{12.25}=3.5$
Question 692 Marks
Find the least number that must be added to $1300$ so as to get a perfect square. Also find the square root of the perfect square.
Answer
View full question & answer→First finding $\sqrt {1300}$ by long division method.
The remainder is $4$. This shows that $36^2< 1300.$
Next perfect square number is $37^2= 1369.$
Hence, the number to be added is $37^2- 1300 = 1369 - 1300 = 69.$
And the square root of the perfect square = $\sqrt {1369}$ $= 37$.
The remainder is $4$. This shows that $36^2< 1300.$
Next perfect square number is $37^2= 1369.$
Hence, the number to be added is $37^2- 1300 = 1369 - 1300 = 69.$
And the square root of the perfect square = $\sqrt {1369}$ $= 37$.
Question 702 Marks
Find the square of the number $42$ without actual multiplication.
Answer
View full question & answer→$42^2= (40 + 2)^2$
$= (40 + 2)(40 + 2)$
$= 40(40 + 2) + 2(40 + 2)$
$= 40^2+ 40 \times 2 + 2\times 40 + 2^2$
$= 1600 + 80 + 80 + 4 = 1764$
$= (40 + 2)(40 + 2)$
$= 40(40 + 2) + 2(40 + 2)$
$= 40^2+ 40 \times 2 + 2\times 40 + 2^2$
$= 1600 + 80 + 80 + 4 = 1764$
Question 712 Marks
Find the greatest $4$-digit number which is a perfect square.
Answer
View full question & answer→Greatest number of $4$-digits $= 9999$
First finding $\sqrt9999$ by long division method.
The remainder is $198$. This shows $99^2$ is less than $9999$ by $198$.
This means if we subtract the remainder from the number, we get a perfect square.
Therefore, the greatest $4$-digit number which is a perfect square is $= 9999 – 198 = 9801$
First finding $\sqrt9999$ by long division method.
The remainder is $198$. This shows $99^2$ is less than $9999$ by $198$.
This means if we subtract the remainder from the number, we get a perfect square.
Therefore, the greatest $4$-digit number which is a perfect square is $= 9999 – 198 = 9801$
Question 722 Marks
Find the square of the number $39$ without actual multiplication.
Answer
View full question & answer→$39^2=(30+9)^2$
$= (30 + 9)(30 + 9)$
$= 30(30 + 9) + 9(30 + 9)$
$= 30^2+30 \times 9+9 \times 30+9^2$
$= 900 + 270 + 270 + 81 = 1521$
$= (30 + 9)(30 + 9)$
$= 30(30 + 9) + 9(30 + 9)$
$= 30^2+30 \times 9+9 \times 30+9^2$
$= 900 + 270 + 270 + 81 = 1521$
Question 732 Marks
Find the least number that must be subtracted from $5607$ so as to get a perfect square. Also find the square root of the perfect square number.
Answer
View full question & answer→First finding $\sqrt{5607}$ by long division method.
We get the remainder $131$. It shows that $74^2$ is less than $5607$ by $131$.
This means if we subtract the remainder from the number, we get a perfect square.
Thus, the least number that must be subtracted from $5607$ so as to get a perfect square is $131$.
And the required perfect square number is $5607 - 131 = 5476$. So, $\sqrt{5476}$ $= 74$.
We get the remainder $131$. It shows that $74^2$ is less than $5607$ by $131$.
This means if we subtract the remainder from the number, we get a perfect square.
Thus, the least number that must be subtracted from $5607$ so as to get a perfect square is $131$.
And the required perfect square number is $5607 - 131 = 5476$. So, $\sqrt{5476}$ $= 74$.