Help with square roots

so we are doing problems like this in our math class but I'm not comprehending how to do them, and the teacher doesn't explain it very well.
2 (square root sign) 1000

or

3 (square root sign) 12 + 4 (square root sign) 3

Please help me!
Thank you so much!

Okay... I'm assuming you're trying to simplify these values.

The first question of 2 times (square root of 1000.)
You need to find all the prime numbers that make up 1000... one way to think of it is
1000 = 10 x 10 x 10 = 2 x 5 x 2 x 5 x 2 x 5 = 2^3 x 5^3 (aka 2 to the third power times 5 to the third power.)
So you know that 2 times (square root of 1000) = (2 to the third power) times (5 to the third power.)
Using square roots, you should get
2 times 2 times 5 times (square root of 2 times 5)
and then simplify this to
20 times (square root of 10.)

For the second problem, we have 3 times (square root of 12) + 4 (square root of 3.)
Using the same method as above,
12 = 3 x 4 = 3 x 2 x 2
and we don't need to break down 3 because it's already a prime number.
Now, we know
3 times (square root of 12) + 4 times (square root of 3)
= 3 times (square root of 3 x 2 x 2) + 4 times (square root of 3)
= 3 times 2 times (square root of 3) + 4 times (square root of 3)
= 6 times (square root of 3) + 4 times (square root of 3)
Finally, that equals 10 times (square root of 3.)

Hope that helps :/

2 times the square root of 1,000

3 times the square root of 12 plus 4 times the square root of 3

You probably have some tables in your book for square roots or directions on how to calculate a square root.

2*sqrt(1000) = 2*10*sqrt(10) = 20*sqrt(10) = 20*3.16227766 = 63.2455532

3*sqrt(12) + 4*sqrt(3) = 3*sqrt(4*3) + 4*sqrt(3) = 6*sqrt(3) + 4*sqrt(3) = 10*sqrt(3) =

10*1.732050808 = 17.32050808

2sqrt(1000)

2sqrt(10)sqrt(100)

2(10)sqrt(10)

20sqrt(10)

3sqrt(12) + 4sqrt(3)

3sqrt(4)sqrt(3) + 4sqrt(3)

3(2)sqrt(3) + 4sqrt(3)

6sqrt(3) + 4sqrt(3)

10sqrt(3)