Squares and Square Roots Test

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Squares and Square Roots Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

Find the atleast number which must be added to each of the following numbers to get a perfect square. Also find the square root of the perfect square numbers.

$$a)525$$

A
4

B
3

C
1

D
6

E
12

Solution

$$i)\ 23^2=529$$
$$\therefore \ $$ it will add $$4$$ to $$525$$ we get $$529$$
which is payout square
$$\therefore \ 525+4=529=23^2$$

$$\therefore 4$$ should be added
Question 2
1 / -0

Which of the following is a Pythagorean triplet?

A
$$8, 6, 10$$

B
$$8, 9, 10$$

C
$$10, 12, 13$$

D
None of these

Solution

"Pythagorean triples" are integer solutions to the Pythagorean Theorem, $$a^2 + b^2 = c^2.$$

$$A.$$ $$8,6,10$$
$$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$$
$$\Rightarrow$$ $$(10)^2=(8)^2+(6)^2$$
$$\Rightarrow$$  $$100=64+36$$
$$\Rightarrow$$  $$100=100$$
$$\therefore$$ $$8,6,10$$ is a Pythagorean triplet

$$B.$$ $$8,9,10$$
$$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$$
$$\Rightarrow$$ $$(10)^2=(8)^2+(9)^2$$
$$\Rightarrow$$  $$100=64+81$$
$$\Rightarrow$$  $$100\ne 146$$
$$\therefore$$ $$8,9,10$$ is not a Pythagorean triplet

$$C.$$ $$10,12,13$$
$$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$$
$$\Rightarrow$$ $$(13)^2=(10)^2+(12)^2$$
$$\Rightarrow$$  $$169=100+144$$
$$\Rightarrow$$  $$100\ne 244$$
$$\therefore$$ $$10,12,13$$ is not a Pythagorean triplet
Question 3
1 / -0

Find $$\sqrt {125}$$ given $$\sqrt {5}=2.23607$$

A
$$11.21$$

B
$$11.38$$

C
$$11.18$$

D
$$11.24$$

Solution

$$\sqrt{125}$$
$$=\sqrt{5\times 5\times 5}$$
$$=5\sqrt{5}$$
$$=5\times 2.23607$$
$$=11.180$$.
Question 4
1 / -0

If $$\sqrt{2}=1.414$$ then the value of $$\sqrt{8}$$ is

A
$$2.828$$

B
$$1.828$$

C
$$2.282$$

D
$$2.288$$

Solution

$$\sqrt{2}=1.414$$(given)
$$\sqrt{8}=\sqrt{2\times 2\times 2}=2\sqrt{2}=2\times 1.414=2.828$$
$$\therefore \sqrt{8}=2.828$$
Question 5
1 / -0

Which of the following numbers are not perfect square?

A
2397

B
121000

C
25008

D
19640

E
All of above

Solution

These all are $$not$$ perfect square numbers because perfect square numbers always ends with $$(0,1,4,5,6,9)$$ and if if last digit is $$0$$ it should be even number of zeros.
Therefore all the given numbers are not perfect square.
Question 6
1 / -0

Simplify : $$(64)^{1/2}$$

A
$$12$$

B
$$2$$

C
$$8$$

D
$$14$$

Solution

$$(64)^{1/2}$$
$$=(8\times 8)^{1/2}$$
$$=(8^2)^{1/2}$$
$$=8^1$$
$$=8$$.
Question 7
1 / -0

Square root of 169 is

A
13

B
14

C
15

D
None of these

Solution
Question 8
1 / -0

Mark the correct alternative of the following.
Which of the following is/are not Pythagorean triplet(s)?

A
$$3, 4, 5$$

B
$$8, 15, 17$$

C
$$7, 24, 25$$

D
$$13, 26, 29$$

Solution

We have to check for pythagorean triplets.

Option (A) $$3, 4, 5$$
It is easy to check that $$3^2 + 4^2 = 5^2$$
$$25 = 25$$
$$3, 4, 5$$ is pythagorean triplet.

Option (B) $$8 , 15 , 17$$
Observe that $$8^2 + 15^2 = 64 + 225$$
$$= 289 $$
$$= 17^2$$
Hence $$8, 15, 17$$ is pythagorean triplet

Option (C) $$7, 24, 25$$
observe that $$7^2 + 24^2 = 49 + 576 $$
$$= 625$$
$$= 25^2$$
So $$7, 24, 25$$ is pythagorean triplet.

Option (D) $$13, 26, 29$$
check that $$13^2 + 26^2 = 169 + 676$$
$$= 845$$
and $$29^2 = 841$$
So $$13^2 + 26^2 \neq 29^2$$

Hence option D is correct.
Question 9
1 / -0

Which of the following number is not a perfect square?

A
$$1444$$

B
$$3136$$

C
$$961$$

D
$$2222$$

Solution

Explanation: According to the property of square, a number ending with $$2,3,7$$ and $$8$$ is not a perfect square.
Hence, $$2222$$ is not a perfect square.
Question 10
1 / -0

Which of the following number is not a perfect square?

A
$$1843$$

B
$$3721$$

C
$$1024$$

D
$$1296$$

Solution

$$(a) 1843$$
Explanation: According to the property of square a number ending with $$2,3,7$$ and $$8$$ is not a perfect square. Hence, $$1843$$ is not a perfect square.

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Re-Attempt Weekly Quiz Competition

Squares and Square Roots Test - 28

Result

Squares and Square Roots Test - 28

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SHARING IS CARING

Question 1

4

3

1

6

12

Solution

Question 2

$$8, 6, 10$$

$$8, 9, 10$$

$$10, 12, 13$$

None of these

Solution

Question 3

$$11.21$$

$$11.38$$

$$11.18$$

$$11.24$$

Solution

Question 4

$$2.828$$

$$1.828$$

$$2.282$$

$$2.288$$

Solution

Question 5

2397

121000

25008

19640

All of above

Solution

Question 6

$$12$$

$$2$$

$$8$$

$$14$$

Solution

Question 7

13

14

15

None of these

Solution

Question 8

$$3, 4, 5$$

$$8, 15, 17$$

$$7, 24, 25$$

$$13, 26, 29$$

Solution

Question 9

$$1444$$

$$3136$$

$$961$$

$$2222$$

Solution

Question 10

$$1843$$

$$3721$$

$$1024$$

$$1296$$

Solution

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