Question 12 Marks
If the square of a number ends with $10$ zeroes$, $how many zeroes will the number have?
AnswerWe know that if a number ends with $n$ zeros Then its square will have $2 n$ zeroes Conversely, if square of a number have $2 \mathrm{n}$ zeros at their ends then the number will have $\mathrm{n}$ zeroes The square of a number ends $10 $ zeroes, then the number will have $\frac{10}{2}=5$ zeroes
View full question & answer→Question 22 Marks
Which of the following numbers will not have $1 ($one$)$ at their unit’s place :$ (i)\ 322\ (ii)\ 572\ (iii)\ 692\ (iv)\ 3212\ (v)\ 2652$
AnswerThe square of the following numbers will not have $1 $ at their units place: as only $(1)^2=1,(9)^2=81$ have $1$ at then units place $322, 572, 2652$ i.e., $(i), (ii)$ and $(v)$
View full question & answer→Question 32 Marks
Seeing the value of the digit at unit$’$s place, state which of the following can be square of a number :
$(i)\ 3051\ (ii)\ 2332\ (iii)\ 5684\ (iv)\ 6908\ (v)\ 50699$
AnswerWe know that the ending digit $($the digit at units place$)$ of the square of a number is $0, 1, 4, 5, 6$, or $9$
So, the following numbers can be squares$: 3051, 5684$, and $50699$ i.e.,$ (i), (iii)$, and$ (v)$
View full question & answer→Question 42 Marks
Without doing the actual addition, find the sum of : $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23$
Answer$1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 +23=$ Sum of first $12 $ odd natural numbers $= 122 = 144$
View full question & answer→Question 52 Marks
Find the square root of : $0.01+\sqrt{0.0064}$
Answer
| |
$0.08$ |
| $8$ |
$0.0064$
$64$ |
| |
$x$ |
$= 0.01 + 0.08 = 0.09$ View full question & answer→Question 62 Marks
Find the square root of : $\frac{1764}{2809}$
Answer
| |
$42$ |
| $4$ |
$1764$
$16$ |
| $82$ |
$164$
$164$ |
| |
$x$ |
| $53$ |
| $5$ |
$2809$
$25$ |
| $103$ |
$309$
$309$ |
| |
$x$ |
Hence, square root of $\sqrt{\frac{1764}{2809}}=\frac{42}{53}$ View full question & answer→Question 72 Marks
Find the value of $\sqrt{5}$ correct to $2$ decimal places; then use it to find the square root of $\sqrt{\frac{3-\sqrt{5}}{3+\sqrt{5}}}$ correct to $2$ significant digits.
Answer$\sqrt{5}=2.236=2.24$
| |
$2.236$ |
| $2$ |
$5.000000$
$4$ |
| $42$ |
$100$
$84$ |
| $443$ |
$1600$
$1329$ |
| $4466$ |
$27100$
$26796$ |
| |
$304$ |
$ \sqrt{\frac{3-\sqrt{5}}{3+\sqrt{5}}}$
$ =\sqrt{\frac{(3-\sqrt{5})((3-\sqrt{5}))}{(3+\sqrt{5})(3-\sqrt{5})}}$
$ =\sqrt{\frac{(3-\sqrt{5})^2}{(3)^2-\sqrt{(5)}^2}}$
$ =\frac{\sqrt{(3-\sqrt{5})^2}}{9-5}$
$ =\sqrt{\frac{3-\sqrt{5}^2}{4}}$
$ =\frac{(3-2.24)}{2}$
$ =\frac{(0.76)}{2}$
$ =0.38$
$ $ View full question & answer→Question 82 Marks
Find the square root of $7 $ correct to two decimal places; then use it to find the value of $\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}$ correct to three significant digits.
Answer$\sqrt{7}=2.645=2.65$
| |
$2.645$ |
| $2$ |
$7.000000$
$4$ |
| $46$ |
$300$
$276$ |
| $524$ |
$2400$
$2096$ |
| $5285$ |
$30400$
$26425$ |
| |
$3975$ |
Now, $\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}$
$=\sqrt{\frac{(4+\sqrt{7})(4+\sqrt{7})}{(4-\sqrt{7})(4+\sqrt{7})}}$
$ =\sqrt{\frac{(4+\sqrt{7})^2}{(4)^2-\sqrt{(7)}^2}}$
$ =\sqrt{\frac{\left(4+\sqrt{7}^2\right)}{16-7}}$
$=\sqrt{\frac{\left(4+\sqrt{7}^2\right)}{9}}$
$ =\frac{4+\sqrt{7}}{3}$
$ =\frac{4+2.65}{3}$
$=\frac{6.65}{3}$
$=2.22$ View full question & answer→Question 92 Marks
For the following, find the least number that must be added so that the resulting number is a perfect square $55078.$
Answer$55078$
| |
$234$ |
| $2$ |
$55078$
$4$ |
| $43$ |
$150$
$129$ |
| $464$ |
$2178$
$1856$ |
| |
$322$ |
Taking square root of $ 55078 $, we find that $322$ has been left
We see that $55078 $ is greater than $(234)^2$ On adding the required number to $55078 $,
we get $(235)^2$ i.e., $55225$
Required number $=55225-55078=147$ View full question & answer→Question 102 Marks
For the following, find the least number that must be added so that the resulting number is a perfect square $7172.$
Answer$7172$
Taking square root of $7172,$ we find that $116$ has been left
We see that $7172$ is greater than $(84)^2$
| |
$84$ |
| $8$ |
$71 72$
$64$ |
| $164$ |
$772$
$656$ |
| |
$116$ |
$∴$ On adding the required number to $7172,$ we get $(85)^2$ i.e.,$7225$
Required number $= 7225 - 7172 = 53$ View full question & answer→Question 112 Marks
For the following, find the least number that must be added so that the resulting number is a perfect square $511.$
Answer$511$
Taking square root of $511,$ we find that $27$ has been left We see that $511$ is greater than $(22)^2$
| |
$22$ |
| $2$ |
$5 11$
$4$ |
| $42$ |
$111$
$84$ |
| |
$27$ |
On adding the required number to $511,$ we get $(23)^2$ i.e., $529$
So, the required number $= 529 – 511 = 18$ View full question & answer→Question 122 Marks
For the following, find the least number that must be subtracted so that the resulting number is a perfect square.$ 23497$
Answer$23497$
Taking square root of $23497,$ we find that $88$ has been left
| |
$153$ |
| $1$ |
$23497$
$1$ |
| $25$ |
$134$
$125$ |
| $303$ |
$997$
$909$ |
| |
$88$ |
$∴$ Least number to be subtracted $= 88$ View full question & answer→Question 132 Marks
For the following, find the least number that must be subtracted so that the resulting number is a perfect square.$1886$
Answer$1886$
Taking square root of $1886$, we find that $37 $ has been left
| |
$43$ |
| $4$ |
$1886 16$ |
| $83$ |
$286$
$249$ |
| |
$37$ |
$∴$ Least number to be subtracted $= 37$ View full question & answer→Question 142 Marks
For the following, find the least number that must be subtracted so that the resulting number is a perfect square. $ 796$
Answer$796$
Taking square root of $796$, we find that $12 $ has been left
| |
$28$ |
| $2$ |
$7 96$
$4$ |
| $48$ |
$396$
$384$ |
| |
$12$ |
$∴$ Least number to be subtracted $= 12$ View full question & answer→Question 152 Marks
Find the square root of $5.2005 $ correct to two places of decimal.
Answer$5.2005$
| |
$2.28$ |
| $2$ |
$5.2005$
$4$ |
| $42$ |
$120$
$84$ |
| $448$ |
$3605$
$3584$ |
| $456$ |
$2100$ |
Required square root $= 2.28$ up to two places of demical. View full question & answer→Question 162 Marks
Find the square root of $245 $ correct to two places of decimal.
Answer$245$
| |
$15.65$ |
| $1$ |
$245$
$1$ |
| $25$ |
$145$
$125$ |
| 306 |
$2000$
$1836$ |
| $3125$ |
$16400$
$15625$ |
| |
$775$ |
Required square root $= 15.65$ up to two places of decimal.
View full question & answer→Question 172 Marks
Find the square root of$: 0.007225$
Answer$0.007225$
| |
$0.085$ |
| $0.8$ |
$0.007225$
$64$ |
| $0.165$ |
$825$
$825$ |
| |
$x$ |
Required square root $= 0.085$ View full question & answer→Question 182 Marks
Find the square root of $: 531.7636$
Answer$531.7636$
| |
$23.06$ |
| $2$ |
$531.7636$
$4$ |
| $43$ |
$131$
$129$ |
| $4606$ |
$2.7636$
$2.7636$ |
| |
$x$ |
Required square root $= 23.06$ View full question & answer→Question 192 Marks
Find the square root of $: 4.2025$
Answer$4.2025$
| |
$2.05$ |
| $2$ |
$4.2025$
$4$ |
| $405$ |
$0.2025$
$0.2025$ |
| |
$x$ |
Required square root $= 2.05$ View full question & answer→Question 202 Marks
Find the square root of $: 27.3529$
Answer$27.3529$
| |
$5.23$ |
| $5$ |
$27.3529$
$25$ |
| $102$ |
$2.35$
$2.04$ |
| $1043$ |
$3129$
$3129$ |
| |
$x$ |
Required square root $= 5.23$ View full question & answer→Question 212 Marks
Find the square root of $: 0.023104$
Answer$0.023104$
| |
$0.152$ |
| $0.1$ |
$0.023104$
$0.01$ |
| .$25$ |
$131$
$125$ |
| $302$ |
$604$
$604$ |
| |
$x$ |
Required square root $= 0.152$ View full question & answer→Question 222 Marks
Find the square root of $: 001225$
Answer$0.001225$
| |
$0.035$ |
| $0.03$ |
$0.001225$
$9$ |
| $0.065$ |
$325$
$325$ |
| |
$x$ |
Required square root $= 0.035$ View full question & answer→Question 232 Marks
Find the square root of $: 0.2916$
Answer$0.2916$
| |
$0.54$ |
| $0.5$ |
$0.2916$
$0.25$ |
| $0.104$ |
$416$
$416$ |
| |
$x$ |
Required square root $= 0.54$ View full question & answer→Question 242 Marks
Find the square root of : $15129$
Answer$15129$
| |
$123$ |
| $1$ |
$15129$
$1$ |
| $22$ |
$51$
$44$ |
| $243$ |
$729$
$729$ |
| |
$x$ |
Required Square root $= 123$ View full question & answer→Question 252 Marks
Find the square root of : $ 7744$
Answer$7744$
| |
$88$ |
| $8$ |
$7744$
$64$ |
| $168$ |
$1344$
$1344$ |
| |
$x$ |
Required square root $= 88$ View full question & answer→Question 262 Marks
Find the least number which must be subtracted from $1205 $ so that the resulting number is a perfect square.
AnswerClearly, if $49$ is subtracted from $1205$, the number will be a perfect square.
| |
$34$ |
| $3$ |
$1205$
$9$ |
| $64$ |
$305$
$256$ |
| |
$49$ |
$\therefore 1205-49=1156$ and $\sqrt{1156}=34$ View full question & answer→Question 272 Marks
Find the square root of: $ 4761$
Answer$4761$
| |
$69$ |
| $6$ |
$4761$
$36$ |
| $129$ |
$1161$
$1161$ |
| |
$x$ |
Required square root $= 69$ View full question & answer→Question 282 Marks
Find the square root of $0.0169.$
Answer$0.0169$
$ =\sqrt{\frac{169}{10000}}$
$ =\frac{13}{100}$
$ =0.13$
View full question & answer→Question 292 Marks
Find the square root of $96 \frac{1}{25}$.
Answer$96 \frac{1}{25}$
$ =\sqrt{\frac{2401}{25}}$
$ =\frac{49}{5} \text { i.e. } 9 \frac{4}{5}$
View full question & answer→Question 302 Marks
Find the square root of $0.1764$
Answer$\sqrt{0.1764}$
$=\sqrt{\frac{01764}{10000}}$
$ =\frac{42}{100}$
$ =0.42 \mathrm{~V}$
View full question & answer→