Question 1012 Marks
Find the square root of the following by long division method: $3226694416$
Answer
Hence, the square root of $3226694416$ is $56804$
View full question & answer→Hence, the square root of $3226694416$ is $56804$
Questions · Page 3 of 3
2 Marks Questions
Question 1022 Marks
Find the squares of the following numbers. $745$
Answer
View full question & answer→$(745)^2$
Here $n = 74$
$\therefore$ $n(n + 1) = 74(74 + 1)$
$= 74 \times 75 = 5550$
$\therefore$ $(745)^2= 555025$
Here $n = 74$
$\therefore$ $n(n + 1) = 74(74 + 1)$
$= 74 \times 75 = 5550$
$\therefore$ $(745)^2= 555025$
Question 1032 Marks
Using prime factorization method, find the following numbers are perfect squares? $189$
Answer
View full question & answer→$189 = 3 \times 3 \times 3 \times 7$
$\begin{array}{c|c} 3& 189 \\ \hline 3 & 63 \\\hline 3&21 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors, $189 = (3 \times 3) \times 3 \times 7$
The factors $3$ and $7$ cannot be paired.
Hence, $189$ is not a perfect square.
$\begin{array}{c|c} 3& 189 \\ \hline 3 & 63 \\\hline 3&21 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors, $189 = (3 \times 3) \times 3 \times 7$
The factors $3$ and $7$ cannot be paired.
Hence, $189$ is not a perfect square.
Question 1042 Marks
Find the square root of the following correct to three places of decimal: $2\frac{1}{2}$
Answer
View full question & answer→We can find the square root up to four decimal places by expanding $2\frac{1}{2}$ into decimal form up to eight digits to the right of the decimal point as shown below, $2\frac{1}{2}=2.50000000$ But,
this is the same with the value $2.5$ in problem (ix).
Hence, the square root of $2\frac{1}{2}$ is $1.581$.
this is the same with the value $2.5$ in problem (ix).
Hence, the square root of $2\frac{1}{2}$ is $1.581$.
Question 1052 Marks
Find the square root of: $38\frac{11}{25}$
Answer
View full question & answer→We know, $\sqrt{38\frac{11}{25}}=\sqrt{\frac{961}{25}}=\frac{\sqrt{961}}{\sqrt{25}}$ Now, let us compute the square roots of the numerator and the denominator separately. $\sqrt{961}=31$ $\sqrt{25}=5$ $\therefore\sqrt{38\frac{11}{25}}=\frac{31}{5}$
Question 1062 Marks
Find the squares of the following numbers: $862$
Answer
View full question & answer→$(862)^2=(800+62)^2$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(800)^2+2 \times 800 \times 62+(62)^2$
$=640000+99200+3844$
$=743044$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(800)^2+2 \times 800 \times 62+(62)^2$
$=640000+99200+3844$
$=743044$
Question 1072 Marks
Find the square root in decimal form:$0.00059049$
Answer
Hence, the square root of $0.00059049$ is $0.0243$
View full question & answer→Hence, the square root of $0.00059049$ is $0.0243$
Question 1082 Marks
Find the least number which must be subtracted from the following numbers to make tham a perfact square: $4401624$
Answer
View full question & answer→Using the long division method,
We can see that $4401624$ is $20$ more than $2098^2$. Hence,$20$ must be subtracted from $4401624$ to get a perfect square.
We can see that $4401624$ is $20$ more than $2098^2$. Hence,$20$ must be subtracted from $4401624$ to get a perfect square.
Question 1092 Marks
Find the square root of the following by long division method:
$291600$
$291600$
Answer
Hence, the square root of $291600$ is $540$
View full question & answer→Hence, the square root of $291600$ is $540$
Question 1102 Marks
Find the squares of the following numbers using the identity $(a+b)^2=a^2+2 a b+b^2: 1001$
Answer
View full question & answer→$(a+b)^2=a^2+2 a b+b^2$
$(1001)^2=(1000+1)^2$
$=(1000)^2+2 \times 1000 \times 1 \times(1)$
$=1000000+2000+1$
$=1002001$
$(1001)^2=(1000+1)^2$
$=(1000)^2+2 \times 1000 \times 1 \times(1)$
$=1000000+2000+1$
$=1002001$
Question 1112 Marks
Find the squares of the following numbers using the identity $(a-b)^2=a^2-2 a b+b^2: 599$
Answer
View full question & answer→$(a-b)^2=a^2-2 a b+b^2$
$(599)^2=(600-1)^2$
$=(600)^2-2 \times 600 \times 1+(1)^2$
$=360000-1200+1$
$=360001-1200$
$=358801$
$(599)^2=(600-1)^2$
$=(600)^2-2 \times 600 \times 1+(1)^2$
$=360000-1200+1$
$=360001-1200$
$=358801$
Question 1122 Marks
Find the squares of the following numbers using the identity $(a-b)^2=a^2-2 a b+b^2: 999$
Answer
View full question & answer→$(a-b)^2=a^2-2 a b+b^2$
$(999)^2=(1000-1)^2$
$=(1000)^2-2 \times 1000 \times 1+(1)^2$
$=1000000-2000+1$
$=10000001-2000$
$=998001$
$(999)^2=(1000-1)^2$
$=(1000)^2-2 \times 1000 \times 1+(1)^2$
$=1000000-2000+1$
$=10000001-2000$
$=998001$
Question 1132 Marks
Find the least number which must be subtracted from the following numbers to make tham a perfact square: $194491$
Answer
View full question & answer→Using the long division method,
We can see that $194491$ is $10$ more than $441^2$. Hence, $10$ must be subtracted from $194491$ to get a perfact square.
We can see that $194491$ is $10$ more than $441^2$. Hence, $10$ must be subtracted from $194491$ to get a perfact square.
Question 1142 Marks
Write the possible unit's digits of the square root of the following numbers. these numbers are odd square roots$? 998001$
Answer
View full question & answer→The unit digit of the number $998001$ is $1.$ So, the possible unit digits are $1$ or $9.$ Note that $998001$ is equal to $(3^3× 37)^2$.
Hence, the square root is an odd number.
Hence, the square root is an odd number.
Question 1152 Marks
Which of the following triplets are pythagorean$? (14, 35, 38)$
Answer
View full question & answer→A triplet $(a, b, c)$ is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.
The two smallest numbers are $12$ and $35.$ The sum of their squares is,
$12^2+35^2=1369$, which is not equal to $38^2=1444$
Hence, $(12, 35, 38)$ is not a Pythagorean triplet.
The two smallest numbers are $12$ and $35.$ The sum of their squares is,
$12^2+35^2=1369$, which is not equal to $38^2=1444$
Hence, $(12, 35, 38)$ is not a Pythagorean triplet.
Question 1162 Marks
Find the squares of the following numbers: $503$
Answer
View full question & answer→$(503)^2=(500+3)^2$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(500)^2+2 \times 500 \times 3+(3)^2$
$=250000+3000+9$
$=253009$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(500)^2+2 \times 500 \times 3+(3)^2$
$=250000+3000+9$
$=253009$
Question 1172 Marks
Using prime factorization method, find the following numbers are perfect squares$? 2048$
Answer
View full question & answer→$2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2$
$\begin{array}{c|c} 2& 2048 \\ \hline 2 & 1024 \\\hline 2&512 \\\hline 2&256 \\\hline 2&128 \\\hline 2&64 \\\hline 2&32 \\\hline2&16 \\\hline2&8 \\\hline2&4 \\\hline2&2 \\\hline&1 \end{array}$
Grouping them into pairs of equal factors, $2048 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × 2$
The last factor, $2$ cannot be paired.
Hence, $2048$ is not a perfect square.
$\begin{array}{c|c} 2& 2048 \\ \hline 2 & 1024 \\\hline 2&512 \\\hline 2&256 \\\hline 2&128 \\\hline 2&64 \\\hline 2&32 \\\hline2&16 \\\hline2&8 \\\hline2&4 \\\hline2&2 \\\hline&1 \end{array}$
Grouping them into pairs of equal factors, $2048 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × 2$
The last factor, $2$ cannot be paired.
Hence, $2048$ is not a perfect square.
Question 1182 Marks
Using prime factorization method, find the following numbers are perfect squares$?$
$2916$
$2916$
Answer
View full question & answer→$2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3$
$\begin{array}{c|c} 2& 2916 \\ \hline 2 & 1458 \\\hline 3&729 \\\hline 3&243 \\\hline 3&81 \\\hline 3&27 \\\hline 3&9 \\\hline 3&3 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
$2916 = (2 × 2) × (3 × 3) × (3 × 3) × (3 × 3)$
There are no left out of pairs. Hence, $2916$ is a perfect square.
$\begin{array}{c|c} 2& 2916 \\ \hline 2 & 1458 \\\hline 3&729 \\\hline 3&243 \\\hline 3&81 \\\hline 3&27 \\\hline 3&9 \\\hline 3&3 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
$2916 = (2 × 2) × (3 × 3) × (3 × 3) × (3 × 3)$
There are no left out of pairs. Hence, $2916$ is a perfect square.