Class 8 Exam  >  Class 8 Tests  >  Olympiad Test: Square And Square Roots - Class 8 MCQ

Olympiad Test: Square And Square Roots - Class 8 MCQ


Test Description

20 Questions MCQ Test - Olympiad Test: Square And Square Roots

Olympiad Test: Square And Square Roots for Class 8 2024 is part of Class 8 preparation. The Olympiad Test: Square And Square Roots questions and answers have been prepared according to the Class 8 exam syllabus.The Olympiad Test: Square And Square Roots MCQs are made for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Square And Square Roots below.
Solutions of Olympiad Test: Square And Square Roots questions in English are available as part of our course for Class 8 & Olympiad Test: Square And Square Roots solutions in Hindi for Class 8 course. Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free. Attempt Olympiad Test: Square And Square Roots | 20 questions in 40 minutes | Mock test for Class 8 preparation | Free important questions MCQ to study for Class 8 Exam | Download free PDF with solutions
Olympiad Test: Square And Square Roots - Question 1

What is the value of x if 

Detailed Solution for Olympiad Test: Square And Square Roots - Question 1

Given 

Olympiad Test: Square And Square Roots - Question 2

What is the greatest number of five digits which is a perfect square?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 2

The greatest number of five digits

1 Crore+ students have signed up on EduRev. Have you? Download the App
Olympiad Test: Square And Square Roots - Question 3

What is the least number which must be subtracted from 6459 to make  a perfect square?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 3



Hence 59 must be subtracted.

Olympiad Test: Square And Square Roots - Question 4

By what least number 384 be multiplied so that the product may be a perfect square?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 4


∴ 384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
so it lacks a 2 and 3

∴ Required number = 6

Olympiad Test: Square And Square Roots - Question 5

What is the smallest number of four digits which is a perfect square?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 5

Consider option (b)

Here 
Clearly 1024 is the smallest number of four digits which is a perfect square.

Olympiad Test: Square And Square Roots - Question 6

What is the greatest number of four digits which is a perfect square?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 6

Greatest number of four digits = 9999

Olympiad Test: Square And Square Roots - Question 7

Find the least number which must be added to 2292 to make it a perfect square.

Detailed Solution for Olympiad Test: Square And Square Roots - Question 7


2292 + 12 = 2304 which is a perfect square.

Olympiad Test: Square And Square Roots - Question 8

Find the smallest number by which 557568 must be divided so that it become a perfect square.

Detailed Solution for Olympiad Test: Square And Square Roots - Question 8

To determine the smallest number by which 557568 must be divided so that it becomes a perfect square, let's factorize 557568 and see the prime factors:

Step 1: Factorize 557568

We can start by dividing 557568 by the smallest prime numbers:

557568÷2=278784(Divide by 2)

278784÷2=139392(Divide by 2)

139392÷2=69696(Divide by 2)

69696÷2=34848(Divide by 2)

34848÷2=17424(Divide by 2)

17424 ÷ 2=8712(Divide by 2)

8712 ÷ 2 = 4356(Divide by 2)

4356÷2=2178(Divide by 2)

2178÷2=1089(Divide by 2, but can’t divide further, stop here with 1089)

To make this exponent even, we must divide by 2 to reduce the exponent to 8 (which is even). Hence, the smallest number by which 557568 should be divided to make it a perfect square is 2.

Answer: 4. 2

Olympiad Test: Square And Square Roots - Question 9

Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 9

396 = 2 × 2× 3 × 3 × 11
To make a perfect square, 11 is multiplied to 396.

Olympiad Test: Square And Square Roots - Question 10

What is the least number which must be added to 6203 to obtain a perfect square ?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 10


6241 – 6203 = 38
38 must be added to 6203 to make a perfect square.

Olympiad Test: Square And Square Roots - Question 11

Find the smallest square number that is divisible by each of the number 8, 15 and 20.

Detailed Solution for Olympiad Test: Square And Square Roots - Question 11

Here LCM of 8, 15, 20 = 120. and
120 = 2  × 2 × 2 × 3 × 5
To make 120 a perfect square, it must be multiplied by 2 × 3 ×5 = 30
120 × 30 = 3600

Olympiad Test: Square And Square Roots - Question 12

What is the least number that must be added to 1300 so as to get a perfect square?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 12

36 × 36 = 1296
37 × 3 7 = 1369
69 must be added to make 1300 as perfect square.

Olympiad Test: Square And Square Roots - Question 13

What is the length of the diagonal of a square whose perimeter is equal to the perimeter of an equilateral triangle of side 4 cm?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 13

Perimeter of an equilateral triangle
= 4 + 4 + 4 = 12 cm

Perimeter of square = 12 cm ⇒ 4 × side = 12 ⇒ Side =  3 cm.
∴    Length of diagonal = 

Olympiad Test: Square And Square Roots - Question 14

The product of two positive numbers is  and one of them is three times the other. Find the larger number.

Detailed Solution for Olympiad Test: Square And Square Roots - Question 14

Let the numbers are x and 3x.


 

Olympiad Test: Square And Square Roots - Question 15

The area of a rectangular field whose length is three times its breadth is 348 m2. What is the perimeter of the field?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 15

Let breadth  be x m
∴ Length = 3x m
Now
 
∴ 
Perimeter = 2 (10.77 + 32.31) = 86.16 m

Olympiad Test: Square And Square Roots - Question 16

Which of the following is not a Pythagorean triplet?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 16

Here 32 + 42 = 52 
         62 + 82 = 102
    22 + 32 ≠ 42
    122 + 352 = 372
∴ (c) is not a Pythagorean triplet.

Olympiad Test: Square And Square Roots - Question 17

The area of a square field is 60025 m2. A man cycles along its boundary at 18 km/hour. In how much time will he return to the starting point?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 17

Speed of cycle = 18 km/hour
18 x 5/18
5m/sec
Area of square = 60025
Side of square =  = 245 m
Perimeter of square = 245 × 4 m
∴    Time taken = 

Olympiad Test: Square And Square Roots - Question 18

What is the length of each side of a square whose area is equal to the area of a rectangle of length 13.6 m and breadth 3.4 meters?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 18

Area of square = Area of rectangle

∴ Side of square =  = 6.8 m

Olympiad Test: Square And Square Roots - Question 19

The perimeter of a square field is 76m. What is its area?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 19

Perimeter of square = 76
⇒    4 × side = 76 ⇒ side = 76/4 = 19
∴ Area of square = 192 = 361 m2

Olympiad Test: Square And Square Roots - Question 20

Which of the following is the square of an even number?

Detailed Solution for Olympiad Test: Square And Square Roots - Question 20

Here 729 = 272, 324 = 182, 441 =  212, 625 = 252
or
Square of an odd number is an odd number.

Information about Olympiad Test: Square And Square Roots Page
In this test you can find the Exam questions for Olympiad Test: Square And Square Roots solved & explained in the simplest way possible. Besides giving Questions and answers for Olympiad Test: Square And Square Roots, EduRev gives you an ample number of Online tests for practice

Top Courses for Class 8

Download as PDF

Top Courses for Class 8