Question

√18*√50-√2.25 (2√2.5)^2+√3*√0.27-√2/√32

Answer 1

√18*√50 - √2,25 =

= √(18*50) - √2,25 =

= √(2*9 * 2*25) - 1,5 =

= 2 * 3 * 5  - 1,5 =

= 30 - 1,5 = 28,5,

(2√2,5)² + √3*√0,27 - √2/√32 =

= 4 * 2,5  +  √0,81  -  √(1/16) =

= 10 + 0,9 - 1/4 =

= 10,9 - 0,25 = 10,65

Answer 2

Let's simplify the expression step by step:

1. √18 = √(9 * 2) = √9 * √2 = 3√2
2. √50 = √(25 * 2) = √25 * √2 = 5√2
3. √2.25 = √(2.25) = 1.5
4. (2√2.5)^2 = (2 * √(2.5))^2 = (2 * √(2.5))^2 = (2 * √(2.5)) * (2 * √(2.5)) = 4 * 2.5 = 10
5. √3 * √0.27 = √(3 * 0.27) = √0.81 = 0.9
6. √2 = √(2)
7. √32 = √(16 * 2) = √16 * √2 = 4√2

Now, let's put the simplified values back into the expression:

3√2 * 5√2 - 1.5 * 10 + 0.9 - √2 / 4√2

To combine the square root terms:

3√2 * 5√2 = 3 * 5 * √(2 * 2) = 15 * √2

Now, the expression becomes:

15√2 - 15 + 0.9 - √2 / 4√2

To combine the remaining terms:

15√2 - √2 / 4√2 = 15√2 - 1/4

Finally, the simplified expression is:

15√2 - 1/4 + 0.9 - 15

Now, combine the constants:

15 - 15 = 0

So the final simplified expression is:

15√2 - 1/4 + 0.9 - 15 = 0.9 - 1/4 - 15√2