Question

How do you simplify: the square root of 200?

Answer 1

`color(green)(=10sqrt2`

Explanation:

• Square root of a number can be simplified by prime factorising the number.

• Prime factorisation involves expressing a number as a product of prime numbers.

(`200` has `2` and `5` as its prime factors.)

So,

`sqrt(200) = sqrt(2*2*2*5*5)`

`sqrt200=sqrt(2^2 *2 *5^2)`

`=2*5sqrt2`

`color(green)(=10sqrt2`