Question

2 √ 48 почему будет 8 √ 3? решите 2 √ 75(чтобы ответ был ? =? √ ? а не одним числом

Answer 1

Ответ:

10√3

Пошаговое объяснение:

Формулы:

$1) \sqrt{x*y} =\sqrt{x} *\sqrt{y} \\\\2) \sqrt{x^{2}} = x$

$2\sqrt{48} =2\sqrt{16*3} = 2\sqrt{16 } *\sqrt{3} =2\sqrt{4^{2} } *\sqrt{3} = 2*4*\sqrt{3} = 8\sqrt{3}$

$2\sqrt{75} =2\sqrt{25*3} = 2\sqrt{25}*\sqrt{3} = 2*\sqrt{5^{2} }*\sqrt{3} = 2*5*\sqrt{3} = 10\sqrt{3}$

Answer 2

To simplify the expression 2√48, we need to find the largest perfect square that divides 48. In this case, the largest perfect square that divides 48 is 16 (which is 4^2). We can then rewrite 48 as 16 * 3. So, we have:

2√48 = 2√(16 * 3)

Now, using the property of square roots (√(a * b) = √a * √b), we can split the square root into two separate square roots:

2√48 = 2√16 * √3

Since √16 = 4, we can simplify further:

2√48 = 2 * 4 * √3 = 8√3

So, the simplified form of 2√48 is 8√3.

Now, let's work on the expression 2√75:

To simplify 2√75, we need to find the largest perfect square that divides 75. In this case, the largest perfect square that divides 75 is 25 (which is 5^2). We can then rewrite 75 as 25 * 3. So, we have:

2√75 = 2√(25 * 3)

Now, using the property of square roots (√(a * b) = √a * √b), we can split the square root into two separate square roots:

2√75 = 2√25 * √3

Since √25 = 5, we can simplify further:

2√75 = 2 * 5 * √3 = 10√3

So, the simplified form of 2√75 is 10√3.