Question

1) √27 - √3; 2) √50 - √2;​

Answer 1

Ответ:

$\sqrt{27} -\sqrt{3} =2\sqrt{3}$

$\sqrt{50} -\sqrt{2} =4\sqrt{2}$

Решение:

Вынесем множитель за знак корня, после чего выполним вычитание:

$\sqrt{27} -\sqrt{3} =\sqrt{9\cdot3} -\sqrt{3} =\sqrt{3^2\cdot3} -\sqrt{3} =3\sqrt{3} -\sqrt{3} =2\sqrt{3}$

$\sqrt{50} -\sqrt{2} =\sqrt{25\cdot2} -\sqrt{2} =\sqrt{5^2\cdot2} -\sqrt{2} =5\sqrt{2} -\sqrt{2} =4\sqrt{2}$

Answer 2

1) √27 - √3:

To simplify this expression, we can simplify each square root individually and then subtract the results. Let's start by simplifying the square roots:

√27 can be simplified as follows: √(9 x 3) = √9 x √3 = 3√3

√3 remains the same.

Now, we can subtract the two simplified square roots:

3√3 - √3 = (3 - 1)√3 = 2√3

Therefore, the simplified expression is 2√3.

2) √50 - √2:

Similar to the previous expression, we will simplify each square root individually and then subtract the results.

√50 can be simplified as follows: √(25 x 2) = √25 x √2 = 5√2

√2 remains the same.

Now, we can subtract the two simplified square roots:

5√2 - √2 = (5 - 1)√2 = 4√2

Therefore, the simplified expression is 4√2.

In summary:

1) √27 - √3 = 2√3 2) √50 - √2 = 4√2