Question

Звільніться дріб від ірраціональності в знаменнику: 10b/2b√5 помогите пожалуйста

Answer 1

$\\ \\ \frac{10b}{2b \sqrt{5} } = \frac{5}{ \sqrt{5} } = \frac{5 \sqrt{5} }{ \sqrt{5} \sqrt{5} } = \frac{5 \sqrt{5} }{5} = \sqrt{5}$

Упростим выражение путем избавления от иррациональности в знаменателе дроби

Сначала сократим 10b и 2b , останется 5 в числителе и 1 в знаменателе,который можно не писать

Далее,зная формулу √n^2= n

(Тоесть, число возведенное к квадрат равно подкоренному выражения, так как квадрат и степень сокращаются)

Домножаем √5 на √5 ,получим √5^2 которая равна 5

Далее сокращаем 5 и в знаменателе, и в числителе, получим ответ :

√5

Answer 2

Simplifying the Expression

To simplify the given expression 10b/2b√5, we can start by breaking it down step by step.

First, let's rewrite the expression in a clearer format: 10b / (2b√5).

Step 1: Canceling Out Common Terms

We can simplify the expression by canceling out common terms in the numerator and the denominator. In this case, we can cancel out the common term "b" from both the numerator and the denominator.

So, the expression becomes: 10 / (2√5).

Step 2: Simplifying the Fraction

Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2 in this case.

So, the simplified expression is: 5 / √5.

Step 3: Rationalizing the Denominator

To remove the radical from the denominator, we can rationalize it by multiplying both the numerator and the denominator by the conjugate of the denominator.

The conjugate of √5 is -√5, so we multiply both the numerator and the denominator by -√5.

The expression becomes: (5 * -√5) / (√5 * -√5).

Step 4: Final Simplified Form

After multiplying, we get: -5√5 / -5.

Finally, we can simplify further by canceling out the common term "-5" from the numerator and the denominator, resulting in the final simplified form: √5.

So, the simplified form of the expression 10b/2b√5 is √5.