Question

1) 1/2√200 - 7√2/49 - √72 2) 1/5√300 - 4√3/16 - √75

Answer 1

1) 1/2√200 - 7√(2/49) - √72 = 0,5·10√2 - 7·√2/7 - 6√2 = 5√2 - √2 - 6√2 = -10√2.

2) 1/5√300 - 4√(3/16) - √75 = 0,2·10√3 - 4√3/4 - 5√3 = 2√3 - √3 - 5√3 = -4√3.

Answer 2

To simplify the given expressions, we can start by simplifying each individual square root term and then perform any necessary arithmetic.

1. Simplifying expression 1:

1/2√200 - 7√2/49 - √72

Step 1: Simplify the square root terms √200 = √(100 * 2) = 10√2 √72 = √(36 * 2) = 6√2

Now the expression becomes:

1/2 * 10√2 - 7√2/49 - 6√2

Step 2: Find a common denominator for the fractions, which is 49.

1/2 * 10√2 * 49/49 - 7√2/49 - 6√2 * 49/49

Step 3: Combine the fractions.

(10/2) * √2 - 7√2/49 - (6 * 49)√2/49

Step 4: Simplify.

5√2 - 7√2/49 - 294√2/49

Step 5: Combine the remaining like terms.

(5 - 7 - 294)√2/49

Step 6: Final answer.

(-296√2)/49

2. Simplifying expression 2:

1/5√300 - 4√3/16 - √75

Step 1: Simplify the square root terms √300 = √(100 * 3) = 10√3 √75 = √(25 * 3) = 5√3

Now the expression becomes:

1/5 * 10√3 - 4√3/16 - 5√3

Step 2: Find a common denominator for the fractions, which is 16.

1/5 * 10√3 * 16/16 - 4√3/16 - 5√3 * 16/16

Step 3: Combine the fractions.

(10/5) * √3 - 4√3/16 - (5 * 16)√3/16

Step 4: Simplify.

2√3 - 4√3/16 - 80√3/16

Step 5: Combine the remaining like terms.

(2 - 4 - 80)√3/16

Step 6: Final answer.

(-82√3)/16

So, the simplified expressions are:

1. (-296√2)/49
2. (-82√3)/16