Squares and Square Roots Test

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Squares and Square Roots Test - 27

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Weekly Quiz Competition

Question 1
1 / -0

Write a Pythagorean triplet whose one number is 8

A
$$8,10,6$$

B
$$15,10,5$$

C
$$63,27,3$$

D
$$80,40,20$$

Solution

$$8^2=64$$
$$\Rightarrow$$ $$100-64=36$$
$$\Rightarrow$$ $$\sqrt{36}=6$$
$$\Rightarrow$$ $$\sqrt{100}=10$$
Let
Hypotenuse $$=10$$ [ Since its greater than $$6$$ and $$8$$ ]
Base $$=8$$ and
Perpendicular $$=6$$

$$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$$ [ Pythagoras theorem ]

$$\Rightarrow$$ $$(10)^2=(6)^2+(8)^2$$
$$\Rightarrow$$ $$100=36+64$$
$$\Rightarrow$$ $$100=100$$
$$\therefore$$ Pythagorean triplet are $$6,8,10$$
Question 2
1 / -0

What will be the unit digits of the square of the following numbers?
$$39$$, $$297$$, $$5125$$, $$7286$$

A
$$9,9,1,6$$

B
$$1,9,5,6$$

C
$$9,2,5,2$$

D
$$3,2,5,7$$

Solution

$$(a)$$The numbers with unit's digits $$1$$ or $$9$$ has its square as $$1$$
$$\therefore\,$$ the unit's digit of square of $$39$$ is $$1$$
$$(b)$$The numbers with unit's digits $$3$$ or $$7$$ has its square as $$9$$
$$\therefore\,$$ the unit's digit of square of $$297$$ is $$9$$
$$(c)$$The numbers with unit's digits $$5$$ has its square as $$5$$
$$\therefore\,$$ the unit's digit of square of $$5125$$ is $$5$$
$$(d)$$The numbers with unit's digits $$4$$ or $$6$$ has its square as $$6$$
$$\therefore\,$$ the unit's digit of square of $$7286$$ is $$6$$
Question 3
1 / -0

Find the square root of $$126736$$ by long division method.

A
$$355$$

B
$$356$$

C
$$366$$

D
$$365$$
Question 4
1 / -0

Find the square root of which of the following numbers will be the least :

A
$$7\dfrac{58}{81}$$

B
$$11\dfrac{14}{25}$$

C
$$10\dfrac{1}{36}$$

D
$$0.3481$$

Solution

$$A.$$

$$7\dfrac{58}{81}=\dfrac{625}{81}$$

$$\Rightarrow$$ $$\sqrt{\dfrac{625}{81}}=\dfrac{25}{9}=2.77$$

$$B.$$

$$11\dfrac{14}{25}=\dfrac{289}{25}$$

$$\Rightarrow$$  $$\sqrt{\dfrac{289}{25}}=\dfrac{17}{5}=3.4$$

$$C.$$

$$10\dfrac{1}{36}=\dfrac{361}{36}$$

$$\Rightarrow$$  $$\sqrt{\dfrac{361}{36}}=\dfrac{19}{6}=3.16$$

$$D.$$

$$0.3481=\dfrac{3481}{10000}$$

$$\Rightarrow$$  $$\sqrt{\dfrac{3481}{10000}}=\dfrac{59}{100}=0.59$$

$$\therefore$$ We can see, $$0.3481$$ has least square root.
Question 5
1 / -0

Find value of $$\sqrt{5184}$$.

A
$$72$$

B
$$52$$

C
$$82$$

D
$$62$$

Solution

$$\sqrt{5184}\\=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3}\\=\sqrt{2^6\times 3^4}\\=2^3\times3^2\\=8\times9=72$$
Question 6
1 / -0

Find the square root by prime factorisation:
i) $$196$$
ii) $$225$$

A
$$14, 25$$

B
$$14, 15$$

C
$$24, 15$$

D
$$24, 25$$

Solution

(1)

$$196=2\times 2\times 7\times 7$$

$$\sqrt{196}=\sqrt{2\times 2\times 7\times 7}$$

$$=\sqrt{2^{2}\times 7^{2}}$$

$$=2\times 7$$
$$=14$$

(2)

$$225=3\times 3\times 5\times 5$$

$$\sqrt{225}=\sqrt{3\times 3\times 5\times 5}$$

$$=\sqrt{3^{2}\times 5^{2}}$$

$$=3\times 5$$
$$=15$$
Question 7
1 / -0

Find the value of $$\sqrt{66049}$$.

A
$$253$$

B
$$257$$

C
$$347$$

D
$$343$$

Solution

The number $$66049$$ can only be divided by $$257$$
$$66049=257\times 257$$
$$66049=(257)^2$$
$$\sqrt{66049}=\sqrt{257^2}$$
$$\therefore$$ $$\sqrt{66049}=257$$
Question 8
1 / -0

A pythagorean triplet whose two numbers are 8 and 10, then third number is

A
$$6$$

B
$$14$$

C
$$16$$

D
$$18$$

Solution

Require pythagorean triplet is (6,8,10) as $$6^2+8^2 = 36+64= 100 = 10^2 $$
Question 9
1 / -0

Which of the following is a perfect square number?

A
257

B
256

C
300

D
None of these

Solution
Question 10
1 / -0

Which of the following is pythagorean triplet?

A
3 ,4 ,5

B
5 ,12 ,13

C
7 ,24 ,25

D
All of these

Solution

$$\textbf{Step-Check option one by one using condition of pythagorian triplet}$$
$$\text{$$a,b$$ and $$c$$ are called pythagorean triplet if}$$ $$a^2+b^2=c^2$$
$$\text{Clearly,}$$ $$3^2+4^2=9+16=25=5^2$$
$$5^2+12^2=25+144=169=13^2$$
$$7^2+24^2=49+576=625=25^2$$
$$\text{Here all three of the given options are satisfy the pythagorean triplet.}$$
$$\textbf{Hence option D is correct}$$

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Squares and Square Roots Test - 27

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Squares and Square Roots Test - 27

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Question 1

$$8,10,6$$

$$15,10,5$$

$$63,27,3$$

$$80,40,20$$

Solution

Question 2

$$9,9,1,6$$

$$1,9,5,6$$

$$9,2,5,2$$

$$3,2,5,7$$

Solution

Question 3

$$355$$

$$356$$

$$366$$

$$365$$

Question 4

$$7\dfrac{58}{81}$$

$$11\dfrac{14}{25}$$

$$10\dfrac{1}{36}$$

$$0.3481$$

Solution

Question 5

$$72$$

$$52$$

$$82$$

$$62$$

Solution

Question 6

$$14, 25$$

$$14, 15$$

$$24, 15$$

$$24, 25$$

Solution

Question 7

$$253$$

$$257$$

$$347$$

$$343$$

Solution

Question 8

$$6$$

$$14$$

$$16$$

$$18$$

Solution

Question 9

257

256

300

None of these

Solution

Question 10

3 ,4 ,5

5 ,12 ,13

7 ,24 ,25

All of these

Solution

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