Squares and Square Roots Test - 1

This is the correct answer.
The smallest number divisible by each of the numbers 8, 9 and 10 is their LCM.

The LCM of 8, 9 and 10 is 2 x 4 x 9 x 5 = 360
Resolving 360 into prime factors,

360 = 2 x 2 x 2 x 3 x 3 x 5
Grouping the factors into pairs of equal factors, we have

360 = (2 x 2) x (3 x 3) x 2 x 5
Hence, there is no factor to form pairs with 2 and 5.

Thus, to make 360 a perfect square, it must be multiplied by 2 x 5 = 10.

Hence, the smallest square number divisible by 8, 9 and 10 is 3600.

This is the correct answer.

Resolving 176 into prime factors, we get
176 = 2 x 2 x 2 x 2 x 11

Grouping the factors into pairs of equal factors, we get
176 = (2 x 2) x (2 x 2) x 11

Hence, the prime factor 2 occurs in pairs, but there is no prime factor to form a pair with 11.

Therefore, the number must be multiplied by 11 so that it becomes a perfect square.

This is the correct answer.
The given number is 575.
Using the identity (a - b)² = a² - 2ab + b², we get
575² = (600 - 25)²
= 600² - 2 x 600 x 25 + 25²
= 360000 - 30000 + 625
= 330625

This is the correct answer.
Using the identity (a - b)² = a² - 2ab + b², we get
189² = (200 - 11)²
= 40000 - 2 x 200 x 11 + 11²
= 40000 - 4400 + 121
= 35721

This is the correct answer.
Using the identity (a + b)² = a² + 2ab + b², we get
211² = (200 + 11)²
= 200² + 2 x 200 x 11 + 11²
= 40000 + 4400 + 121
= 44521

This is the correct oanswer.
Using the identity (a + b)² = a² + 2ab + b², we get
509² = (500 + 9)²
= (500)² + 2 x 500 x 9 + (9)²
= 250000 + 9000 + 81
= 259081