Question

Сократите дробь: √20-√30 √10-√15

Answer 1

1)2корень из5 - корень из 30
2)-0.7

Answer 2

To simplify the expression, we can rationalize the denominators (i.e., eliminate the square roots from the denominators). This can be done by multiplying both the numerator and denominator of each fraction by the conjugate of the denominator. The conjugate of a square root expression of the form √a ± √b is √a ∓ √b.

Let's simplify the given expression step by step:

1. √20 - √30 / √10 - √15

First, let's rationalize the denominator:

Multiply the numerator and denominator by the conjugate of the denominator (√10 + √15):

[√20 - √30] * [√10 + √15] / [√10 - √15] * [√10 + √15]

2. (√20 * √10) + (√20 * √15) - (√30 * √10) - (√30 * √15) / (√10 * √10) - (√10 * √15) - (√15 * √10) + (√15 * √15)

3. (√200) + (√300) - (√300) - (√450) / (√100) - (√150) - (√150) + (√225)

4. (√200) - (√450) / (√100) + (√225)

Next, simplify the square roots:

√200 = √(100 * 2) = 10√2 √450 = √(225 * 2) = 15√2 √100 = 10 √225 = 15

Now, the expression becomes:

(10√2 - 15√2) / (10 + 15)

Combine like terms:

-5√2 / 25

Finally, simplify the fraction:

-√2 / 5

So, the simplified expression is -√2 / 5.