Question

Избавьтесь от иррациональности в знаменателе дроби: 1) 5(черта)2√6; 2)x+2(черта)√4-х^2; 3) 1(черта) 3+2√2; 4)√√17 + √8 (черта) √√17-√8. Помогите пожалуйста! Нужно срочно!

Answer 1

Смотри ))))))))))))))))))))))))))))))))))

Answer 2

Simplifying Fractions with Irrational Denominators

To simplify fractions with irrational denominators, we need to rationalize the denominator. This means eliminating any irrational numbers from the denominator by multiplying both the numerator and denominator by a suitable expression. Let's go through each of the given fractions and simplify them:

1) 5/2√6:

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is 2√6. This will eliminate the square root from the denominator.

Multiplying the numerator and denominator by 2√6, we get:

(5/2√6) * (2√6/2√6) = (10√6)/(2 * 6) = (10√6)/12 = (5√6)/6

Therefore, the simplified form of 5/2√6 is (5√6)/6.

2) (x + 2)/√(4 - x^2):

To simplify this fraction, we need to rationalize the denominator. The denominator contains a square root and a difference of squares. We can simplify it by factoring the denominator as (2 - x)(2 + x).

Multiplying the numerator and denominator by the conjugate of the denominator, which is √(4 - x^2), we get:

((x + 2)/√(4 - x^2)) * (√(4 - x^2)/(√(4 - x^2))) = ((x + 2)√(4 - x^2))/(4 - x^2)

Therefore, the simplified form of (x + 2)/√(4 - x^2) is ((x + 2)√(4 - x^2))/(4 - x^2).

3) 1/(3 + 2√2):

To simplify this fraction, we need to rationalize the denominator. The denominator contains a sum of a rational number and an irrational number. We can simplify it by multiplying both the numerator and denominator by the conjugate of the denominator, which is (3 - 2√2).

Multiplying the numerator and denominator by (3 - 2√2), we get:

(1/(3 + 2√2)) * ((3 - 2√2)/(3 - 2√2)) = (3 - 2√2)/(9 - 8) = (3 - 2√2)/1 = 3 - 2√2

Therefore, the simplified form of 1/(3 + 2√2) is 3 - 2√2.

4) √√17 + √8/(√√17 - √8):

To simplify this fraction, we need to rationalize the denominator. The denominator contains a difference of square roots. We can simplify it by multiplying both the numerator and denominator by the conjugate of the denominator, which is (√√17 + √8).

Multiplying the numerator and denominator by (√√17 + √8), we get:

((√√17 + √8)/(√√17 - √8)) * ((√√17 + √8)/(√√17 + √8)) = (√√17 + √8)(√√17 + √8)/(√√17 - √8)(√√17 + √8)

Expanding the numerator and denominator, we get:

(√√17 * √√17) + (√√17 * √8) + (√8 * √√17) + (√8 * √8) / ((√√17 * √√17) - (√√17 * √8) - (√8 * √√17) + (√8 * √8))

Simplifying further, we get:

17 + √(17 * 8) + √(8 * 17) + 8 / (17 - √(17 * 8) - √(8 * 17) + 8)

Therefore, the simplified form of √√17 + √8/(√√17 - √8) is (17 + 2√136 + 8)/(17 - 2√136 + 8).

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