Squares and Square Roots Test

Result

Squares and Square Roots Test - 25

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Which least number must be subtracted to $$1025$$ to make a perfect square? (Use Long division method).

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

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
$$\downarrow$$
$$32$$
$$3$$
$$\overline{10}$$ $$\overline{25}$$
$$9$$
$$62$$
$$125$$
$$124$$

$$1\leftarrow$$ Remainder
The remainder is 1. it represents that the square of $$32$$ is less than $$1025$$ by $$1$$.
Therefore, a perfect square will be obtained by subtracting $$1$$ from the given number $$1025$$.
So, perfect square $$= 1025 - 1$$
$$ = 1024$$
Question 2
1 / -0

Find the square root of 67.24 using long division method.

A
8.2

B
8.3

C
8.1

D
8.4

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
$$\downarrow$$
8.2
8
$$\overline{67}$$.$$\overline{24}$$
64
______
1.62
3.24
3.24
______

0 $$\leftarrow$$ Remainder
$$\sqrt{67.24} = 8.2$$
Question 3
1 / -0

Which least number must be subtracted to 899 to make a perfect square? (Use Long division method).

A
55

B
56

C
57

D
58

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
$$\downarrow$$
29
2
$$\overline{8}$$ $$\overline{99}$$
4
49
499
441

58 $$\leftarrow$$ Remainder
The remainder is 58. it represents that the square of 29 is less than 899 by 58.
Therefore, a perfect square will be obtained by subtracting 58 from the given number 899.
So, perfect square = 899 - 58 = 841
Question 4
1 / -0

Find the square root of 84.64 using long division method.

A
$$9.1$$

B
$$9.2$$

C
$$9.3$$

D
$$9.4$$
Question 5
1 / -0

Evaluate: $$\sqrt{10}$$ correct up to one place of decimal.

A
3.1

B
3.16

C
3.162

D
3.1622

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.
Hence, $$\sqrt{10} = 3.1$$ (correct upto one decimal place)
Question 6
1 / -0

Estimate the square root of $$500.$$

A
$$22.35$$

B
$$20.3$$

C
$$21.4$$

D
$$23.6$$
Solution
- The two consecutive perfect squares among which $$500$$ lies are $$484(22^2)$$ and $$529(23^2)$$
  So, the whole number part of the square root of $$500$$ is $$ 22.$$
- The decimal part can be determined by the formula: $$\dfrac{\text{Given number – Smaller perfect square}}{ \text{Greater perfect square – smaller perfect square} }=\dfrac{500-484}{529-484}=\dfrac{16}{45}=0.35$$
- So, the estimated value of the square root of $$500$$ by the approximation method is $$22.35.$$
Question 7
1 / -0

Find the approximate value of $$\sqrt{5245}$$.

A
70.5

B
72.3

C
71.8

D
79.2

Solution

$$72^2$$ = 5184
$$73^2$$ = 5329
In between this two squares, 5245 is placed.
So average of $$\frac{72 + 73}{2}= 72.5$$
Then, $$72.5^2 = 5256.25$$
So, $$\sqrt{5245} \approx 72.3$$
Question 8
1 / -0

What is the square root of 506.25 using long division method?

A
22.5

B
21.4

C
23.4

D
25.3

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
$$\downarrow$$
22.5
2
$$\overline{5}$$ $$\overline{06}$$.$$\overline{25}$$
4
_______
42
106
84
_______
44.5
22.25
22.25
_______
0 $$\leftarrow$$ Remainder
$$\sqrt{50.625} = 22.5$$
Question 9
1 / -0

What is the square root of $$292.41$$ using long division method?

A
17.1

B
17.2

C
17.3

D
17.4

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.
Hence, $$\sqrt{29.241} = 17.1$$

Question 10

1 / -0

What is the square root of $$156.25$$ using long division method.

$$12.3$$

$$12.5$$

$$12.4$$

$$12.7$$

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 $$\downarrow$$ 12.5
1	$$\overline{1}$$ $$\overline{56}$$.$$\overline{25}$$ 1 _______
22	56 44 _______
24.5	12.25 12.25 ______ 0 $$\leftarrow$$ Remainder

$$\sqrt{156.25} = 12.5$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Divisor $$\downarrow$$	Quotient $$\downarrow$$ $$32$$
$$3$$	$$\overline{10}$$ $$\overline{25}$$ $$9$$
$$62$$	$$125$$ $$124$$
	$$1\leftarrow$$ Remainder

Divisor $$\downarrow$$	Quotient $$\downarrow$$ 8.2
8	$$\overline{67}$$.$$\overline{24}$$ 64 ______
1.62	3.24 3.24 ______
	0 $$\leftarrow$$ Remainder

Divisor $$\downarrow$$	Quotient $$\downarrow$$ 29
2	$$\overline{8}$$ $$\overline{99}$$ 4
49	499 441
	58 $$\leftarrow$$ Remainder

Divisor $$\downarrow$$	Quotient $$\downarrow$$ 22.5
2	$$\overline{5}$$ $$\overline{06}$$.$$\overline{25}$$ 4 _______
42	106 84 _______
44.5	22.25 22.25 _______ 0 $$\leftarrow$$ Remainder

Squares and Square Roots Test - 25

Result

Squares and Square Roots Test - 25

Score

-

Rank

-

SHARING IS CARING

Question 1

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 2

8.2

8.3

8.1

8.4

Solution

Question 3

55

56

57

58

Solution

Question 4

$$9.1$$

$$9.2$$

$$9.3$$

$$9.4$$

Question 5

3.1

3.16

3.162

3.1622

Solution

Question 6

$$22.35$$

$$20.3$$

$$21.4$$

$$23.6$$

Solution

Question 7

70.5

72.3

71.8

79.2

Solution

Question 8

22.5

21.4

23.4

25.3

Solution

Question 9

17.1

17.2

17.3

17.4

Solution

Question 10

$$12.3$$

$$12.5$$

$$12.4$$

$$12.7$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.