Verified answer

You should be able to see it is immediately divisible by 100. As the digits sum to 9, it's also divisible by 3

So we can say quite easily

that 1800 = 18 x 100

= (2 x 3^2) x (10^2)

and it follows that

√1800 = √2 x √(3^2) x √(10^2)

= 30√2

What do you mean by "has a perfect square" ? You must realise that 1800 is not a perfect square, and you cannot do anything to make it one.

If by "simplify" you mean reduce it to a smaller square root times an integer, you start by factorizing 1800 into the smallest primes :

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5, which you can write as

= 2 x 2² x 3² x 5² (notice that I have made sure that all the exponents are even numbers where possible. There were three 2's, but I write it as 2 x 2² rather than 2³)

The basic definition of square root means that √2² = 2 and so on. Therefore

√(2² x 3² x 5²) = 2 x 3 x 5 = 30

and √(2 x 2² x 3² x 5²) = 30√2, which is as far as you can go unless you express √2 in decimal form.

Think of numbers which are squares that 1800 is divisable by

9 (3*3) and 100 (10*10) are two such numbers

pick one such square factor and simplify continue until the result cannot be divided by any squares

√1800 = √(18*100) (√100 = 10)

=10√18

=10√(9*2) (√9 = 3)

=10*3√2

=30√2

Simply use the perfect squares

4 * 450 = 1800

450 = 9*50

50 = 2*25

4 = 2 * 2 9 = 3 * 3 25 = 5*5

sqrt(1800) = 2*3*5*sqrt(2)

Factor 1800 completely into a product of primes:

1800 = (2^3)*(3^2)*(5^2), so sqrt(1800) = 2*3*5*sqrt(2)=

30*sqrt(2).

hmm..900 x 2 = 1800.

√1800 = √(900 x 2) = (√900) x √2) = 30√2

sqrt 1800

sqrt 100 *sqrt 18

10 sqrt 18

10 sqrt 9*sqrt 2

30 sqrt 2