Question

Освободитесь от иррациональности в дроби а) 10/√7-3 б)3/√аСРОЧНО​

Answer 1

Ответ:

А) 10/√7-3 = 10/√4 = 10/2 = 5

Б) 3/√а = 3√а/√а√а = 3√а/а

Удачи!

Answer 2

Simplifying Irrational Fractions

To simplify irrational fractions, we need to rationalize the denominator. This means getting rid of any square roots or other irrational terms in the denominator. Let's look at the two examples you provided:

a) 10/√7-3

To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of √7-3 is √7+3. Multiplying the numerator and denominator by √7+3, we get:

10(√7+3)/(√7-3)(√7+3)

Expanding the denominator using the difference of squares formula, we have:

10(√7+3)/(√7)^2 - (3)^2

Simplifying further, we get:

10(√7+3)/(7-9)

And finally:

-10(√7+3)/2

So, the simplified form of the fraction 10/√7-3 is -5(√7+3).

b) 3/√a

To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of √a is √a. Multiplying the numerator and denominator by √a, we get:

3√a/√a√a

Simplifying further, we have:

3√a/a

So, the simplified form of the fraction 3/√a is 3√a/a.

I hope this helps! Let me know if you have any further questions.