Squares and Square Roots Test

Result

Squares and Square Roots Test - 6

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

What is the sum of first 75 odd numbers?

A
150

B
1503

C
5425

D
5625

Solution

Sum of first n odd numbers = n²
Sum of first 75 odd numbers = (75)²= 5625
Question 2
1 / -0

What is the value of 'a' in the expression 2423 2425 = a² - 1?

A
2000

B
4242

C
2424

D
2422

Solution

2423 x 2425 = a² - 1 = (a - 1) (a + 1)
(2424 - 1)(2424 + 1) = (a - 1)(a + 1)
This gives a = 2424
Question 3
1 / -0

What is the smallest number by which 7776 must be divided to get a perfect square?

A
6

B
2

C
3

D
1

Solution

7776 =
Since two digits (2 and 3) are not in pairs, the smallest number by which 7776 must be divided to get a perfect square is 2 x 3 = 6
Question 4
1 / -0

Aman has a square park of area 506.25 m². What will be the cost of fencing the park at a rate of Rs. 30 per metre?

A
Rs. 3600

B
Rs. 905.25

C
Rs. 2700

D
Rs. 270.25

Solution

Area of square park = 506.25 m²
We know, Area = (Side)²
Side = = 22.5 m
Perimeter = 4 Side = 4 22.5 = 90 m
Cost of fencing 1 m = Rs. 30
Cost of fencing 90 m = Rs. 2700
Question 5
1 / -0

Which of the following numbers will end with the digit 1?

A
(1823)²

B
(73219)²

C
(3637)²

D
(18238)²

Solution

9² = 81
Since 9² ends with the digit 1, so (73219)² will also end with the digit 1. None of the other options ends up as a number whose unit's digit is 1.
Question 6
1 / -0

How many numbers are there between (1275)² and (1276)²?

A
2499

B
2550

C
2000

D
1050

Solution

There are 2n numbers lying between n² and (n + 1)².
Here, n = 1275
n + 1 = 1276
2n = 2 ×1275 = 2550
Question 7
1 / -0

A number when squared increases by 506. Find the number.

A
31

B
29

C
23

D
19

Solution

Let the number be x.
So, x² - x - 506 = 0
So, x = 23
Question 8
1 / -0

The length of the hypotenuse of an isosceles right-angled triangle is 30 m. What is the length of the other two sides of the triangle?

A
23.3 m

B
21.21 m

C
19.6 m

D
17.7 m

Solution

x² + x² = 900
2x² = 900
x² = 450
x =
x = 21.21 m
Question 9
1 / -0

If , then what is the value of x?

A
2.261

B
0.2261

C
22.61

D
0.0261

E
None of these

Solution

(8.69)² = 75.5161
On squaring both sides of the given equation, we get
75.29 + x = 75.5161
x = 0.2261
Question 10
1 / -0

If , what is the value of x?

A
1

B
2

C
5

D
4

Solution

4/3 = 1 + x/3
1/3 = x/3
x = 1
Question 11
1 / -0

What is the least perfect square which is exactly divisible by 2, 4 and 8?

A
16

B
8

C
1

D
4

Solution

LCM (2, 4, 8) = 8, but 8 is not a perfect square.
So, the least perfect square which is exactly divisible by 2, 4 and 8 = 16
Question 12
1 / -0

How many natural numbers lie between 1² and 100²?

A
99

B
100

C
101

D
9999

Solution

Value of 1² = 1
Value of 100² = 10000
Therefore, difference = 10000 - 1 = 9999.
So, 9999 natural numbers lie between 1² and 100².
Question 13
1 / -0

The area of a square is 1296 square units. What is the ratio of sum of all the sides to the square root of a side?

A
144 : 1

B
36 : 1

C
24 : 1

D
1296 : 9

Solution

Let the side of the square be x units.
Then, x² = 1296

x = 36
So one side of square = 36 units
Sum of all the sides = 144 units
Square root of one side = 6 units
So the required ratio = 144 : 6 = 24 : 1
Question 14
1 / -0

What is the units digit of the following expression?

(233)² x (332)² x (444)²

A
9

B
4

C
6

D
7

Solution

The given expression: (233)² x (332)² x (444)²
Solve the expression step by step.
Units digit of (233)² = 9 as it has 3 at ones place.
Units digit of (332)² = 4 as it has 2 at ones place.
Units digit of (444)² = 6 as it has 4 at ones place.

Now, we can find the units digit of the given expression by multiplying the ones digits of each part.
9 x 4 x 6 = 216
Therefore, the given expression has 6 at ones place.
Question 15
1 / -0

Find the value of P + Q : 1 + P - Q, where P and Q are {/} and {/}, respectively.

A
1 : 4

B
4 : 1

C
1 : 3

D
3 : 1

Solution

Firstly, simplify the values of P and Q.
P =/ =/ = 6/3 = 2
Q =/} =/} = 6/3 = 2
Therefore, P + Q = 2 + 2 = 4
1 + P - Q = 1 + 2 - 2 = 1;
Therefore, the required value of P + Q : 1 + P - Q is 4 : 1.