Squares and Square Roots Test

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Squares and Square Roots Test - 30

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Question 1
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Some questions and their alternative answer are given. Select the correct alternative . Out of the following which is the pythagorean triplet?

A
$$(1, 5 , 10 )$$

B
$$( 3 , 4 , 5 )$$

C
$$( 2, 2, 2)$$

D
$$(5, 5, 2)$$

Solution

(A) In the triplet ( 1, 5, 10 )
$$1^{2}=1,5^{2}=25,10^{2}=100 \ and \ 1+25 =26\neq 100$$
The square of largest number is not equal to the sum of the square of the other two numbers.
$$\therefore (1, 5, 10)$$ is not pythagorean triplet.
In the triplet (3 , 4 , 5)
$$3^{2}= 9 , 4^{2} = 16 , 5^{2} =25 \ and \ 9 + 16 = 25$$
The square of the largest number is not equal to the sum of the square of the other two numbers.
$$\therefore (2,2,2)$$ is not a pythgorean triplet.
In the triplet (5,5,2)
$$2^{2}=4,5^{2}=25,5^{2}=25 \ and \ 4 +25 = 29\neq 25$$
The square of the largest number is not equal to the sum of the square of the other two numbers.
$$\therefore (5,5,12)$$ is not a pythagprean triplet
Hence, the correct option is $$(3,4,5)$$
Question 2
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Some question and their alternative answer are given. Select the correct alternative . Out of the dates given below which date constitutes a pythagorean triplet ?

A
$$15/08/17$$

B
$$16/08/16$$

C
$$3/5/17$$

D
$$4/9/15$$

Solution

(A) In the triplet $$15 / 08 / 17$$
$$15^{2}=225,8^{2}=64,17^{2}=289 \ and \ 225+64=289$$ The square of the largest number is equal to the sum of the sum of square of the two numbers.
$$\therefore 15/08/17$$ is a pythsgorean triplet

(B) In the triplet $$16/08/16$$
$$ 16^{2}=256,8^{2}=64,16^{2}=256 \ and \ 256+64=320\neq 256$$
The square of the largest number is not equal to the sum of the squares of the other two numbers.
$$\therefore 16/08/16 $$ is not a pythagorean triplet

(C)In the triplet $$3/5/17$$
$$3^{2}=9,5^{2}= 25, 17^{2} = 289 \ and \ 9 + 25 = 34\neq 289$$
The square of the largest number is not equal to the sum of the squares of the other two numbers
$$\therefore 3/5/17$$ is not a pythagorean triplet

(D)In the triplet $$4/9/15$$
$$4^{2}=16,9^{2}=81,15^{2}=225 \ and \ 16+81=97\neq 225$$
The square of the largest number is not equal to the sum of the square of the other two numbers
$$\therefore 4/9/15$$ is not a pythagorea triplet.
Hence, the correct option is $$15/08/17$$
Question 3
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Choose the correct option:
The number of perfect squares from $$1$$ to $$500$$ is

A
$$1$$

B
$$16$$

C
$$22$$

D
$$25$$

Solution
Question 4
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Choose the correct option:
The last digit of a perfect square number can never be ___.

A
$$1$$

B
$$3$$

C
$$5$$

D
$$9$$

Solution

As we know that, all the perfect square number ends with $$1,4,5,6,9$$ and $$0$$

So, the last digit of a perfect square can never be $$3.$$

Hence, $$Op-B$$ is correct.
Question 5
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Out of the following which is a Pythagorean triplet?

A
$$(5, 12, 14)$$

B
$$(3, 4, 2)$$

C
$$(8, 15, 17)$$

D
$$(5, 5, 2)$$

Solution
Question 6
1 / -0

Estimate the square root of $$300$$.

A
$$12.44$$

B
$$16.66$$

C
$$17.32$$

D
$$18.54$$

Solution
Question 7
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Which of the following numbers is a perfect square?

A
$$36$$

B
$$81$$

C
$$37$$

D
Both $$(A)$$ and $$(B)$$

Solution
Question 8
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Find the square root: $$\sqrt { 4562 }$$

A
66.52

B
67.52

C
66.53

D
67.54

Solution
Question 9
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Estiamate the square root of $$850$$

A
$$29.15$$

B
$$30.21$$

C
$$98.23$$

D
$$23.11$$

Solution

The square root of $$850$$ is $$\sqrt {850}=\sqrt {25 \times 34}=5\sqrt {34}$$
Square root of $$34$$ lie between $$5$$ and $$6$$.
square of $$5.5$$ is $$30.25$$
Now, we can say that square root of $$34$$ lie between $$5.5$$ and $$6$$.
Now, square of $$5.75$$ is $$33.06$$
So, square root of $$34$$ lie between $$5.75$$ and $$6$$.
Now, we have to choose the number $$5.85$$
$$(5.85)^2=34.225$$ which is greater than $$34$$ and close to $$34$$
So, assume a number $$5.84$$.
$$(5.84)^2=34.1056$$
$$(5.83)^2=33.9889$$
Hence, we can say that square root of 34 lie between $$5.83$$ and $$5.84$$.
So, $$5\times 5.83=29.15$$.
Question 10
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$$n-$$ similar balls each of weight $$w$$ when weighed in pairs, the sum of the weights of all the possible pairs is $$120$$ and then they are weighed in triplets, the sum of the weights comes out to be $$480$$ for all possible triplets. Then $$n4$ is equal to

A
$$5$$

B
$$10$$

C
$$15$$

D
$$20$$