Question

7√7-√112=? (26 баллов)!​

Answer 1

Ответ:

3√7

Объяснение:

7√7 - √112 = 7√7 - √4*28=7√7 - √4*4*7=7√7 - 4√7=3√7

Answer 2

To simplify the expression 7√7 - √112, we need to simplify the square roots and then perform the subtraction.

First, let's simplify the square roots:

√7 can't be simplified further because 7 is not a perfect square.

To simplify √112, we can factor 112 into its prime factors: 112 = 2 * 2 * 2 * 2 * 7 = 2^4 * 7.

Using the property of square roots, we can split the square root of a product into the product of the square roots:

√112 = √(2^4 * 7) = √2^4 * √7 = 2^2 * √7 = 4√7.

Now we can substitute the simplified square roots back into the expression:

7√7 - √112 = 7√7 - 4√7.

Since both terms have the same square root (√7), we can combine them by subtracting the coefficients:

7√7 - 4√7 = (7 - 4)√7 = 3√7.

Therefore, 7√7 - √112 simplifies to 3√7.