Question

4 - √80 ______ 1 - √5

Answer 1

Відповідь:

4

Пояснення:

Оскільки $\sqrt{80} = \sqrt{16*5} =\sqrt{4^{2} *5}$

Answer 2

Ответ:

$\frac{4 - \sqrt{80} }{1 - \sqrt{5} } = \frac{4 - 4 \sqrt{5} }{1 - \sqrt{5} } = \frac{(1 + \sqrt{5}) \times (4 - 4 \sqrt{5}) }{(1 + \sqrt{5} ) \times (1 - \sqrt{5}) } = \frac{4 + 4 \sqrt{5} - 4 \sqrt{5} - 20 }{1 - 5} = \frac{ - 16}{ - 4} = 4$

Answer 3

To simplify the expression $\frac{4 - \sqrt{80}}{1 - \sqrt{5}}$, you can start by rationalizing the denominators. To do that, you can multiply both the numerator and denominator by the conjugate of the denominator:

$\frac{4 - \sqrt{80}}{1 - \sqrt{5}} \cdot \frac{1 + \sqrt{5}}{1 + \sqrt{5}}$

Now, let's simplify the expression step by step:

1. Distribute the numerators:

$(4 - \sqrt{80})(1 + \sqrt{5})$

2. Use the distributive property to multiply each term:

$4 \cdot 1 + 4 \cdot \sqrt{5} - \sqrt{80} - \sqrt{80} \cdot \sqrt{5}$

3. Simplify the products:

$4 + 4\sqrt{5} - \sqrt{80} - \sqrt{400}$

4. Further simplify by finding the square roots:

$4 + 4\sqrt{5} - 4\sqrt{5} - 20$

5. Combine like terms:

$4 - 20$

6. Finally, subtract to get the simplified result:

$-16$

So, $\frac{4 - \sqrt{80}}{1 - \sqrt{5}} = -16$.