Prime Factorisation Quiz

The very next number that is a perfect square next to 90 is 100
The smallest number that must be added is 10 to make it a perfect square.

Prime factorisation of 3825:
3 x 3 x 5 x 5 x 17 = 3² × 5² × 17¹
Exponent of 3 is 2

324/18 = 18; 648/18 = 36; 972/18 = 84; 756/42
36 is a perfect square

Prime factorisation of 90: 2 x 3 x 3 x 5
= 2¹ x 3² x 5¹
Multiply by 2 × 5 = 10 to make all powers even

The prime factorisation of 6 is 2 x 3
The cube of 6 will thus be = 2³ x 3³
The exponent of 2 is thus 3

The prime factorisation of 108 = 2 x 2 x 3 x 3 x 3
= 2² x 3³
To make all the exponents even 108 must be divided by 3 to get a perfect square.

Perfects squares close to 200 = 169, 196, 225
Number which is less than 200 and closest to 200 is 196
Subtract 4 from 200 to get a perfect square

Factorisation of 64 = 2 x 2 x 2 x 2 x 2 x 2
= 2⁶ = (2²)³ = (2³)²

LCM of 2 and 5=10
Prime factorisation of 10 = 2¹ x 5¹
To make a perfect cube, the exponents of all primes must be multiples of 3.
So we need: 2³ x 5³
The cube root of the smallest cube divisible by both 2 and 5 is 10.

LCM of 2 and 4 is 4
Prime factorisation of 4 = 2²
To make a perfect cube, the exponents of all primes must be multiples of 3.
So we need: 2³
The cube root of the smallest cube divisible by both 2 and 4 is 2.