Squares and Square Roots Test

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Squares and Square Roots Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

Mr. Hansraj wants to find the least number of boxes to be added to get a perfect square. He already has $$7924$$ boxes with him. How many more boxes are required?

A
$$819$$

B
$$412$$

C
$$419$$

D
$$176$$

Solution

Find square root by long division method.
$$\therefore \sqrt {7924}$$ = $$89.01$$

Hence, the perfect square number smaller than $$7924$$ is
$$89^2 = 7921$$
The next perfect square no. is $$90^2 = 8100$$

So, $$8100 - 7924 = 176$$
Therefore, the man needs $$176$$ more boxes in order to get a perfect square number.
So, option D is correct.
Question 2
1 / -0

Find the value of $$\sqrt {25}$$.

A
$$5$$

B
$$-\sqrt {5}$$

C
$$\sqrt {3}$$

D
None of these

Solution

$$\sqrt {25} = \sqrt {5\times 5} = 5$$
Question 3
1 / -0

Estimate: $$\sqrt { 60 } $$

A
$$7.7$$

B
$$7$$

C
$$7.2$$

D
$$7.5$$

Solution

$$60$$ is in between two perfect squares: $$49$$, which is $${7}^{2}$$ and $$64$$ which is $${8}^{2}$$. The difference between $$64$$ and $$49$$ is $$15$$ so $$60$$ is little more than $$\cfrac{2}{3}$$ of the way toward $$64$$ from $$49$$. A reasonable estimate for $$\sqrt {60}$$, then would be about $$7.7$$ which is a little more than $$\cfrac{2}{3}$$ toward $$8$$ from $$7$$.
Question 4
1 / -0

What least number must be added to $$4812$$ to make the sum a perfect square? (Use Long division method).

A
$$86$$

B
$$88$$

C
$$89$$

D
$$85$$

Solution

The following steps are used to find the square root by long division method:
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
$$69$$
$$6$$
$$\overline{48}$$ $$\overline{12}$$
$$\underline{36} \underline{\ }$$
$$129$$
$$1212$$
$$\underline{1161}$$

$$51$$
Here, the remainder $$=51$$

We observe here $$69^2 < 4812 < 70^2$$
The required number to be added $$=70^2 - 4812$$
$$= 4900 - 4812$$
$$= 88$$
Therefore, $$88$$ must be added to $$4812$$ to make it a perfect square.
Question 5
1 / -0

What is the Pythagorean triplets whose one member is $$20$$?

A
$$20, 97, 99$$

B
$$20, 99, 101$$

C
$$20, 197, 199$$

D
$$20, 199, 201$$

Solution

For any natural numbers $$m > 1, 2m$$, $$m^{2} - 1$$, $$m^{2} + 1$$ forms a Pythagorean triplet.
If we take $$m^2 + 1 = 20$$, then $$m^2 = 19$$
The value of m will not be an integer.
If we take $$m^2 - 1 = 20$$, then $$m^2 = 21$$
Again the value of m will not be an integer.
Let $$2m = 20$$
$$=> m = 10$$
$$\therefore 2m = 2 \cdot 10 = 20$$
$$m^{2} - 1$$ = $$10^{2} - 1=99$$
and
$$m^{2} + 1$$ = $$10^{2} + 1=101$$

Therefore, the Pythagorean triplets are $$20, 99, 101.$$
Question 6
1 / -0

Identify which one of the following numbers are Pythagorean triplets?

A
$$12, 35, 37$$

B
$$15, 102, 106$$

C
$$10, 23, 26$$

D
$$14, 28, 50$$

Solution

Taking the case of $$12, 35, 37$$
On squaring each number, we get
$$12^2=144$$
$$35^2 = 1225$$
$$37^2=1369$$

Now, $$12^2+35^2 = 144 + 1225 = 1369$$ $$=37^2$$

$$\therefore 12^2+35^2=37^2$$

Hence, $$12, 35, 37$$ are Pythagorean triplets.
Question 7
1 / -0

$$10,24$$ and __ will form a Pythagorean triplets.

A
$$25$$

B
$$26$$

C
$$27$$

D
$$28$$

Solution

We know that Pythagorean triplets will satisfy the condition, $$a^2+b^2=c^2$$
$$c^2=10^2+24^2\\=100+576\\=676$$
$$\Rightarrow c=26$$
Thus $$10, 24$$ and $$26$$ form a Pythagorean triplet
Question 8
1 / -0

A non-perfect square ends in 2, 3, 7 or ___.

A
4

B
5

C
0

D
8

Solution

A non-perfect square ends in 2, 3, 7 or 8.
Question 9
1 / -0

Find the square root of $$12.25$$ using long division method.

A
$$3.2$$

B
$$3.4$$

C
$$3.5$$

D
$$3.1$$

Solution

The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
3.5
3
$$\overline{12}$$.$$\overline{25}$$
9
______
6.5
3.25
3.25
______

0 $$\leftarrow$$ Remainder
$$\sqrt{12.25} = 3.5$$
Question 10
1 / -0

What least number must be added to 700 to make the sum a perfect square? (Use Long division method).

A
25

B
26

C
28

D
29

Solution

The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
26
2
$$\overline{7}$$ $$\overline{00}$$
4
46
300
276

24$$\leftarrow$$ Remainder

We observe here $$26^2 < 700 < 27^2$$
The required number to be added = $$27^2 - 700$$
= 729 - 700
= 29
Therefore, 29 must be added to 700 to make it a perfect square.

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Re-Attempt Weekly Quiz Competition

Divisor $$\downarrow$$	Quotient $$\downarrow$$ $$69$$
$$6$$	$$\overline{48}$$ $$\overline{12}$$ $$\underline{36} \underline{\ }$$
$$129$$	$$1212$$ $$\underline{1161}$$
	$$51$$

Divisor $$\downarrow$$	Quotient $$\downarrow$$ 3.5
3	$$\overline{12}$$.$$\overline{25}$$ 9 ______
6.5	3.25 3.25 ______
	0 $$\leftarrow$$ Remainder

Divisor $$\downarrow$$	Quotient $$\downarrow$$ 26
2	$$\overline{7}$$ $$\overline{00}$$ 4
46	300 276
	24$$\leftarrow$$ Remainder

Squares and Square Roots Test - 24

Result

Squares and Square Roots Test - 24

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SHARING IS CARING

Question 1

$$819$$

$$412$$

$$419$$

$$176$$

Solution

Question 2

$$5$$

$$-\sqrt {5}$$

$$\sqrt {3}$$

None of these

Solution

Question 3

$$7.7$$

$$7$$

$$7.2$$

$$7.5$$

Solution

Question 4

$$86$$

$$88$$

$$89$$

$$85$$

Solution

Question 5

$$20, 97, 99$$

$$20, 99, 101$$

$$20, 197, 199$$

$$20, 199, 201$$

Solution

Question 6

$$12, 35, 37$$

$$15, 102, 106$$

$$10, 23, 26$$

$$14, 28, 50$$

Solution

Question 7

$$25$$

$$26$$

$$27$$

$$28$$

Solution

Question 8

4

5

0

8

Solution

Question 9

$$3.2$$

$$3.4$$

$$3.5$$

$$3.1$$

Solution

Question 10

25

26

28

29

Solution

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