Squares And Square Roots Test

Result

Squares And Square Roots Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

What is the value of 100² - 99²by observing the given pattern?

2² - 1² = 2 + 1
3² - 2² = 3 + 2

A
199

B
100

C
99

D
88

Solution

2² - 1² = 2 + 1
3² - 2² = 3 + 2

100² - 99² = 100 + 99 = 199
Question 2
1 / -0

The ratio of the marks of four students is 2 : 3 : 5 : 6, such that the sum of their squares is 10,656. Find the marks of the four students, respectively.

A
6, 9, 15 and 36

B
12, 18, 30 and 36

C
24, 36, 60 and 72

D
48, 72, 120 and 144.

Solution

The given ratio is 2 : 3 : 5 : 6.
So, let the marks be 2x, 3x, 5x and 6x.

(2x)² + (3x)² + (5x)² + (6x)² = 10,656
4x² + 9x² + 25x² + 36x² = 10,656

74x²= 10,656
x²= 10656 ÷ 174
x²= 144
x = 12

The marks of the students are 24, 36, 60 and 72, respectively.