The product of two numbers is 4046 and their quotient is 7 2 . Find the numbers.

Let x and y are two numbers. Product of two numbers = 4046 ∴ x y = 4046 ⇒ x = 4046 y ........(i) Quotient = 7 2 ∴ x y = 7 2 ⇒ 4046 y y = 7 2 (Using (i)) ⇒ 4046 y 2 = 7 2 ⇒ y 2 = 4046 × 2 7 ⇒ y 2 = 1156 ⇒ y 2 = 2 × 2 × 17 × 17 ⇒ y = 2 × 2 × 17 × 17 = 2 × 17 = 34 Put y = 34 in (i), we get x = 4046 34 = 119 Therefore, required two numbers are x = 119 and y = 34 .

E M B I B E

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.3>Q 3

MEDIUM

8th CBSE

IMPORTANT

Earn 100

Find the square root by prime factorisation method. $9801$

Important Questions on Squares and Square Roots

MEDIUM

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 1

Find the smallest square number which is divisible by each of the numbers

6, 9

and

15

.

HARD

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 2

Find the smallest number by which

5392

must be divided so that the quotient is a perfect square. Find the square root of the quotient.

EASY

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 3

The product of two numbers is

2197

. If one of the numbers is

13

times the other number, find the numbers.

MEDIUM

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 4

A rectangular field is

81 m

long and

49 m

wide. A square field has the same area as that of the rectangular field. Find the side of the square field.

MEDIUM

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 5

A school collected

₹ 11025

as fees from its students. If each student paid as much money as there were students in the school, how many students were there in the school?

EASY

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 6

Find the smallest number by which

27783

must be multiplied so that it becomes a perfect square.

MEDIUM

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 7

The product of two numbers is

4046

and their quotient is

\frac{7}{2}

. Find the numbers.

MEDIUM

8th CBSE

IMPORTANT

Step by Step>Chapter 3 - Squares and Square Roots>EXERCISE 3.4>Q 8

Find the smallest number by which $2925$ should be divided so as to get a perfect square. Also, find the square root of the square number so obtained.