Squares and Square Roots Test

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Squares and Square Roots Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.
$$252$$

A
$$3;42$$

B
$$7;42$$

C
$$7;30$$

D
$$2;42$$

Solution

By prime factorisation we get
$$252=\underline{2\times2}\times\underline{3\times3}\times7$$
$${ \underline { 2\mid 252 } }\\ { \underline { 2\mid 126 } }\\ { \underline { 3\mid 63 } }\\ { \underline { 3\mid 21 } }\\ { \underline { 7\mid 7 } }\\ \; \; \mid 1$$
It is clear that in order to get a perfect square, one more $$7$$ is required.
So, the given number should be multiplied by $$7$$ to make the product a perfect square.
$$\therefore\;252\times7=1764$$ is a perfect square.
Thus, $$1764=\underline{2\times2}\times\underline{3\times3}\times\underline{7\times7}$$
$$\therefore\;\sqrt{1764}=2\times3\times7=42$$
Question 2
1 / -0

Without doing any calculation, find the numbers which are surely not perfect squares:
$$153$$
$$257$$
$$408$$
$$441$$

A
$$153,\,257\;and\;441$$ are surely not perfect squares.

B
$$441,\,257\;and\;408$$ are surely not perfect squares.

C
$$153,\,441\;and\;408$$ are surely not perfect squares.

D
$$153,\,257\;and\;408$$ are surely not perfect squares.
Question 3
1 / -0

A gardener wants to plant $$17956$$ trees and arranges them in such a way that there are as many rows as there are trees in a row. What is the number of trees in a row?

A
$$144$$

B
$$136$$

C
$$154$$

D
$$134$$

Solution

$$\textbf{Step 1: Assume the no. of trees and use the information given}$$

$$\text{Let the no. of trees in a row be x.}$$

$$\therefore x\times x = 17956$$

$$\Rightarrow x^2 = 17956$$

$$\Rightarrow x = \sqrt{17956}$$

$$\Rightarrow x = \sqrt{2\times 2\times 67\times 67}$$

$$\Rightarrow x = 2\times 67$$

$$\Rightarrow x = 134$$

$$\textbf{Hence, the required no. of trees = 134, option - D is the correct answer.}$$
Question 4
1 / -0

The largest number of $$5$$ digits, which is perfect square is

A
$$99999$$

B
$$99764$$

C
$$99976$$

D
$$99856$$

Solution

The largest number of 5 digits $$= 99999$$
Required number $$= (99999 - 143) = 99856 = 316^2$$
Question 5
1 / -0

What could be the possible 'one's' digit of the square root of each of the following numbers?
$$9801$$
$$99856$$

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

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

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

D
$$2\;or\;8\;;\;5\;or\;0$$

Solution

As we know that all the perfect square number ends with $$1,4,9,6,5,00$$
Thus, the possible unit digit of square root of 9801 is either 1 or 9 and it will odd square root and the possible unit digit of square root of 99856 is either 4 or 6 and it will have even square root.
Question 6
1 / -0

Find the square root of each of the following numbers by division method:
$$2304$$
$$4489$$
$$3481$$

A
$$38;67;59$$

B
$$48;57;59$$

C
$$48;67;69$$

D
$$48;67;59$$

Solution

By long division, we have
$$\therefore\;\sqrt{2304}=48$$
$$\;\;\;\;\;\;\;\;\;\;48\\ \overline { 4\;\;\mid \;\;\bar {23 } \bar { 04 } } \\ { { \; \; \;\;\; \mid -16 } }\\ { \overline { 88\mid\;\;\;\;704 } }\\ \; \; \; { \underline { \;\;\mid -704 } }\\ \; \;\;\;\mid \; \; 0$$
By long division, we have
$$\therefore\;\sqrt{4489}=67$$
$$\;\;\;\;\;\;\;\;\;\;67\\ \overline { \;\;6\; \mid \;\;\bar {44 } \bar { 89 } } \\ { { \; \; \; \; \; \;\mid -36 } }\\ { \overline { 127\mid\;\; 889 } }\\ \; \; \; { \underline { \; \;\;\mid -889 } }\\ \; \; \; \;\; \mid \; \; 0$$
By long division, we have
$$\therefore\;\sqrt{3481}=59$$
$$\;\;\;\;\;\;\;\;\;\;59\\ \overline { \;\;5\; \mid \;\;\bar{34 } \bar{ 81 } }\\ { { \; \; \; \; \; \;\mid -25 } }\\ { \overline { 109\mid\;\; 981 } }\\ \; \; \; { \underline { \; \;\;\mid -981 } }\\ \; \; \; \;\; \mid \; \; 0$$
Question 7
1 / -0

The students of class VII of a school denoted $$Rs. 2401$$ in all, for Prime Minister's National Relief Fund. Each student denoted as many rupees as the number of students in the class. Find the number of students in the class.

A
$$47$$

B
$$51$$

C
$$49$$

D
$$53$$

Solution

Let $$x$$ be the number of students in the class.
Therefore, total money denoted by students
$$=Rs.\;(x\times x)=Rs.\;x^2$$. But it is given as $$Rs.\;2401$$.
$$\therefore\;x^2=2401$$
$$\Rightarrow\;x=\sqrt{2401}$$
$${ \underline { 7\mid 2401 } }\\ { \underline { 7\mid 343 } }\\ { \underline { 7\mid 49 } }\\ { \underline { 7\mid 7 } }\\ \; \; \mid 1$$
$$=\sqrt{\underline{7\times7}\times\underline{7\times7}}$$
$$=7\times7=49$$.
Question 8
1 / -0

Which one of the following can't be the square of natural number ?

A
$$143642$$

B
$$27859$$

C
$$57896$$

D
$$27896$$

Solution

As we know that all the perfect square number ends with $$1,4,9,6,5,00$$
$$\therefore$$ 143642 is not the square of natural number because it ends with 2.

Question 9

1 / -0

Find the square root of $$10$$, correct to four places of decimal.

$$3.4623$$

$$3.1023$$

$$3.1693$$

$$3.1623$$

Solution

.....................................	$$3.16227$$ ...........................
$$3$$ $$+3$$	$$10$$ $$9$$
$$61$$ $$+1$$	$$100$$ $$61$$
$$626$$ $$+6$$	$$3900$$ $$3756$$
$$6322$$ $$+2$$	$$14400$$ $$12644$$
$$63242$$ $$+2$$ ------------- $$632447$$	$$175600$$ $$126484$$ --------------- $$4911600$$ $$4427129$$

$$\sqrt{10}=3.16227\simeq 3.1623$$
$$\therefore$$ The square root of $$10$$ correct to four places of decimal is $$3.1623$$

Question 10
1 / -0

What least number must be substracted from $$176$$ to make it a perfect square?

A
$$16$$

B
$$10$$

C
$$7$$

D
$$4$$

Solution

$$176$$ is not a perfect square .
$$13^{2} = 169 < 176 $$
$$176-169=7$$
Therefore, $$7$$ need to subtract for make perfect square.

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Squares and Square Roots Test - 16

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Squares and Square Roots Test - 16

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Question 1

$$3;42$$

$$7;42$$

$$7;30$$

$$2;42$$

Solution

Question 2

$$153,\,257\;and\;441$$ are surely not perfect squares.

$$441,\,257\;and\;408$$ are surely not perfect squares.

$$153,\,441\;and\;408$$ are surely not perfect squares.

$$153,\,257\;and\;408$$ are surely not perfect squares.

Question 3

$$144$$

$$136$$

$$154$$

$$134$$

Solution

Question 4

$$99999$$

$$99764$$

$$99976$$

$$99856$$

Solution

Question 5

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

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

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

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

Solution

Question 6

$$38;67;59$$

$$48;57;59$$

$$48;67;69$$

$$48;67;59$$

Solution

Question 7

$$47$$

$$51$$

$$49$$

$$53$$

Solution

Question 8

$$143642$$

$$27859$$

$$57896$$

$$27896$$

Solution

Question 9

$$3.4623$$

$$3.1023$$

$$3.1693$$

$$3.1623$$

Solution

Question 10

$$16$$

$$10$$

$$7$$

$$4$$

Solution

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