Question

1/2√200 - 7√2/49 - √72

Answer 1

1)Cократить: 5√2 - 5 √2/7(только 2 в корне,а не всё выражение) - 6√2
2)Привести подобные члены: 5√2 -√2 -6√2
3)-2√2
4) ≈-2,82843

Answer 2

To simplify the expression, let's first simplify each term:

1. Simplify √200: √200 = √(100 * 2) = 10√2

2. Simplify 7√2/49: To simplify the fraction, divide the numerator and denominator by their greatest common divisor (GCD). In this case, GCD(7, 49) = 7. 7√2/49 = (7/7) * √2/7 = √2/7

3. Simplify √72: √72 = √(36 * 2) = 6√2

Now, the expression becomes:

1/2 * 10√2 - √2/7 - 6√2

Next, let's find a common denominator for the terms with √2:

The common denominator is 2 * 7 = 14.

1/2 * 10√2 = 5√2 (multiplied by 14/14) √2/7 = (√2 * 2)/14 = 2√2/14 -6√2 = -6√2 (already in the right form)

Now, the expression becomes:

5√2 - 2√2/14 - 6√2

To add or subtract terms with the same radical, you can combine their coefficients:

(5 - 2/14 - 6)√2

Now, let's calculate the coefficient:

5 - 2/14 - 6 = 5 - 1/7 - 6 = 5 - 1/7 - 42/7 = 5 - 43/7 = (35 - 43)/7 = -8/7

So, the simplified expression is:

-8/7 √2