Squares and Square Roots Test

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Squares and Square Roots Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is a pythagorean triplet?

A
$$(2,\,3,\,5)$$

B
$$(5,\,7,\,9)$$

C
$$(6,\,9,\,11)$$

D
$$(8,\,15,\,17)$$

Solution

$$\textbf{Step1-Check each option which satisfy the condition of Pythagorean triplet}$$
$$\text{(a,b,c) will be a Pythagorean triplet if its satisfies the condition } a^2+b^2=c^2$$
$$\text{Here, we will check the option on by one till we get the answer}$$
$$\text{In option A we have (a,b,c) = (2,3,5)}$$
$$\Rightarrow 2^2+3^2=5^2$$
$$\Rightarrow 4+9=25$$
$$\Rightarrow 13\neq 25$$
  $$\text{Hence option A is not correct}$$

$$\text{In option B we have (a,b,c) = (5,7,9)}$$
$$\Rightarrow 5^2+7^2=9^2$$
$$\Rightarrow 25+49=81$$
$$\Rightarrow 74 \neq 81$$
  $$\text{Hence option B is not correct}$$

$$\text{In option C we have (a,b,c) = (6,9,11)}$$
$$\Rightarrow 6^2+9^2=11^2$$
$$\Rightarrow 36+81=121$$
$$\Rightarrow 117\neq 121$$
  $$\text{Hence option C is not correct}$$

$$\text{In option D we have (a,b,c) = (8,15,17)}$$
$$\Rightarrow 8^2+15^2=17^2$$
$$\Rightarrow 64+225=286$$
$$\Rightarrow 286=286$$
  $$\text{Hence option D is correct}$$

$$\textbf{Hence option D is correct}$$
Question 2
1 / -0

Check whether $$1152$$ is a perfect square. If not, then find the least number by which it should be divided so that, the quotient becomes a perfect square. Also, find the square root of the quotient.

A
$$2; 24$$

B
$$3; 24$$

C
$$2; 19$$

D
$$3; 19$$

Solution

$$1152=\underline{2\times2}\times\underline{2\times2}\times\underline{2\times2}\times2\times\underline{3\times3}$$
All the prime factors except $$2$$ can be paired.
Thus $$1152$$ is not a perfect square
Thus, we should divide $$1152$$ by $$2$$ to get the perfect square.
$$1152\div2=576$$
$$576=\underline{2\times2}\times\underline{2\times2}\times\underline{2\times2}\times\underline{3\times3}$$
Thus, the required least number is $$2\;and\;\sqrt{576}=24$$.
Question 3
1 / -0

Find the square root of each of the following correct to three places of decimal.
$$17$$
$$1.7$$
$$2.5$$
$$\displaystyle\frac{7}{8}$$

A
$$4.153\;;\;1.304\;;\;1.581\;;\;0.935$$

B
$$4.123\;;\;1.304\;;\;1.581\;;\;0.995$$

C
$$4.123\;;\;1.304\;;\;1.581\;;\;0.935$$

D
$$4.123\;;\;1.304\;;\;1.501\;;\;0.935$$

Solution

$$17$$

$$4.123$$
$$4$$
$$+4$$ $$17$$
$$16$$
$$822$$
$$+2$$ $$100$$
$$81$$
$$8243$$ $$1900$$
$$1644$$
$$25600$$
$$24729$$

$$871$$
$$\therefore$$ The square root of $$17=4.123$$

$$1.7$$
$$0$$ $$1.303$$
$$1$$
$$+1$$ $$1.7$$
$$1$$
$$23$$
$$+3$$ $$70$$
$$69$$
$$2603$$ $$10000$$
$$7809$$
$$1191$$

$$\therefore$$ The square root of $$1.7=1.303$$

$$2.5$$
$$0$$ $$1.581$$
$$1$$
$$+1$$ $$2.5$$
$$1$$
$$25$$
$$+5$$ $$150$$
$$125$$
$$308$$
$$+8$$ $$2500$$
$$2464$$
$$3161$$ $$3600$$
$$3161$$

$$439$$
$$\therefore$$ The square root of $$2.5=1.581$$

$$\frac{7}{8}$$
$$8$$ $$70$$
$$64$$ $$0.875$$
$$60$$
$$56$$
$$40$$
$$40$$

$$0$$

$$0.935$$
$$0$$ $$0.875$$
$$0$$
$$9$$
$$9$$ $$87$$
$$81$$
$$183$$
$$+3$$ $$650$$
$$549$$
$$1865$$ $$10100$$
$$9325$$
$$925$$
$$\therefore$$ The square root of $$\frac{7}{8}=0.935$$
Question 4
1 / -0

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained.
$$525$$
$$1750$$

A
$$ 4,23;14,48$$

B
$$ 4,27;14,42$$

C
$$ 4,23;14,42$$

D
$$ 4,27;14,48$$

Solution

We try to find out the square root of $$525$$.
$$\;\;\;\;\;\;\;22\\ \overline { 2\; \; \mid \;\;\bar { 5 }\bar { 25 } } \\ { { \; \; \; \; \; \mid -4 } }\\ { \overline { 42\mid\;\; 125 } }\\ \; \; \; { \underline { \; \; \mid -84 } }\\ \; \; \; \; \mid \; \; 41$$
We observe that
$$(22)^2\,<\,525\,<\,(23)^2$$
The required number to be added
$$=(23)^2-525$$
$$=529-525=4$$
$$\therefore$$ Required perfect square number
$$=525+4=529$$
Clearly, $$\sqrt{529}=23$$.
We try to find out the square root of $$1750$$
$$\;\;\;\;\;\;\;41\\ \overline { 4\; \; \mid \;\;\bar { 17 }\bar { 50 } } \\ { { \; \; \; \; \; \mid -16 } }\\ { \overline { 81\mid\;\; 150 } }\\ \; \; \; { \underline { \; \; \mid -81 } }\\ \; \; \; \; \mid \; \; 69$$
We observe that $$(41)^2\,<\,1750\,<\,(42)^2$$.
The required number to be added
$$=(42)^2-1750$$
$$=1764-1750$$
$$=14$$
$$\therefore$$ Required perfect square number
$$=(1750+14)=1764$$
Clearly, $$\sqrt{1764}=42$$.
Question 5
1 / -0

What could be the possible one's digits of the square root of the following numbers?
$$9801$$
$$99856$$
$$99800$$
$$657666025$$

A
$$1\;or\;9\;;\;4\;or\;6\;;\;0\;;\;5$$

B
$$2\;or\;8\;;\;4\;or\;6\;;\;0\;;\;5$$

C
$$1\;or\;9\;;\;2\;or\;8\;;\;0\;;\;5$$

D
$$1\;or\;9\;;\;4\;or\;6\;;\;5\;;\;0$$

Solution

As we know that all the perfect square number ends with $$1,4,9,6,5,00$$
$$9801 \Rightarrow$$ Possible one's digits $$=1\;or\;9\;\;(\because\;1\times1=1.9\times9=81)$$
$$99856 \Rightarrow$$ Possible one's digits $$=4\;or\;6$$
$$99800 \Rightarrow$$ Possible one's digit $$=0$$
$$657666025 \Rightarrow$$ Possible one's digit $$=5$$
Question 6
1 / -0

Which one of the following cannot be the square of a natural number ?

A
$$30976$$

B
$$75625$$

C
$$28561$$

D
$$143642$$

Solution

As we know that all the perfect square number ends with $$1,4,9,6,5,00$$
So, the square of a natural number never ends in $$ 2$$
$$\therefore 143642$$ is not the square of a natural number.
Question 7
1 / -0

The square root of an odd number

A
need not be odd

B
is odd

C
is even

D
cannot be determined

Solution

The square root of an odd number is odd number. We can check this by taking examples as follows:
$$\sqrt[2]{25}=5$$
Square root of odd number, $$25$$ is a odd number $$5$$.

$$\sqrt[2]{49}=7$$
Square root of odd number, $$49$$ is a odd number $$7$$.

Hence, we can say that the square root of odd number is odd. Option C is correct.
Question 8
1 / -0

Write a Pythagorean triplet whose one member is $$16$$ :

A
$$25, 49$$

B
$$25, 61$$

C
$$63, 65$$

D
None of these
Question 9
1 / -0

What is the smallest number by which 338 is multiplied or divided to make a perfect square?

A
13

B
4

C
6

D
2

Solution

The number $$338$$ is not a perfect square itself.
$$338 = 2\times 169 $$
When we divide it by $$2$$, the quotient left is $$169$$ which is a square of $$13$$.
Therefore, divide it by $$2$$.
Answer is Option $$D$$
Question 10
1 / -0

Write a Pythagorean triplet whose one member is 14:

A
36, 64

B
48, 50

C
8, 6

D
17, 20

Solution

Let us assume 2 m=14 therefore m=7
Now $$ \displaystyle m^{2}+1=7^{2}+1=49+1=50 $$
And $$ \displaystyle m^{2}-1=7^{2}-1=49-1=48 $$
Test : $$ \displaystyle14^{2}+48^{2}=196+1304=2500=50^{2} $$
Hence the triplet is 14,48 and 50 Answer

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Re-Attempt Weekly Quiz Competition

	$$4.123$$
$$4$$ $$+4$$	$$17$$ $$16$$
$$822$$ $$+2$$	$$100$$ $$81$$
$$8243$$	$$1900$$ $$1644$$
	$$25600$$ $$24729$$ $$871$$

$$0$$	$$1.303$$
$$1$$ $$+1$$	$$1.7$$ $$1$$
$$23$$ $$+3$$	$$70$$ $$69$$
$$2603$$	$$10000$$ $$7809$$
	$$1191$$

$$0$$	$$1.581$$
$$1$$ $$+1$$	$$2.5$$ $$1$$
$$25$$ $$+5$$	$$150$$ $$125$$
$$308$$ $$+8$$	$$2500$$ $$2464$$
$$3161$$	$$3600$$ $$3161$$ $$439$$

$$8$$	$$70$$ $$64$$	$$0.875$$
	$$60$$ $$56$$
	$$40$$ $$40$$ $$0$$

	$$0.935$$
$$0$$	$$0.875$$ $$0$$
$$9$$ $$9$$	$$87$$ $$81$$
$$183$$ $$+3$$	$$650$$ $$549$$
$$1865$$	$$10100$$ $$9325$$
	$$925$$

Squares and Square Roots Test - 17

Result

Squares and Square Roots Test - 17

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SHARING IS CARING

Question 1

$$(2,\,3,\,5)$$

$$(5,\,7,\,9)$$

$$(6,\,9,\,11)$$

$$(8,\,15,\,17)$$

Solution

Question 2

$$2; 24$$

$$3; 24$$

$$2; 19$$

$$3; 19$$

Solution

Question 3

$$4.153\;;\;1.304\;;\;1.581\;;\;0.935$$

$$4.123\;;\;1.304\;;\;1.581\;;\;0.995$$

$$4.123\;;\;1.304\;;\;1.581\;;\;0.935$$

$$4.123\;;\;1.304\;;\;1.501\;;\;0.935$$

Solution

Question 4

$$ 4,23;14,48$$

$$ 4,27;14,42$$

$$ 4,23;14,42$$

$$ 4,27;14,48$$

Solution

Question 5

$$1\;or\;9\;;\;4\;or\;6\;;\;0\;;\;5$$

$$2\;or\;8\;;\;4\;or\;6\;;\;0\;;\;5$$

$$1\;or\;9\;;\;2\;or\;8\;;\;0\;;\;5$$

$$1\;or\;9\;;\;4\;or\;6\;;\;5\;;\;0$$

Solution

Question 6

$$30976$$

$$75625$$

$$28561$$

$$143642$$

Solution

Question 7

need not be odd

is odd

is even

cannot be determined

Solution

Question 8

$$25, 49$$

$$25, 61$$

$$63, 65$$

None of these

Question 9

13

4

6

2

Solution

Question 10

36, 64

48, 50

8, 6

17, 20

Solution

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