Question

1) √7-√2)(√7+√2) 2) (√5-2)² 3) √3(2√3+√12) 4) 4√2+√50-√18

Answer 1

1. 5
2. 9-4 корень5
3. 12
4. 6 корень2

Answer 2

Let's simplify each of these expressions step by step:

1. √7 - √2)(√7 + √2)

To simplify this expression, we can use the difference of squares formula: (a - b)(a + b) = a^2 - b^2.

In this case, a = √7 and b = √2.

(√7 - √2)(√7 + √2) = (√7)^2 - (√2)^2 = 7 - 2 = 5

So, the simplified expression is 5.

2. (√5 - 2)²

To simplify this expression, we can use the formula for squaring a binomial: (a - b)² = a² - 2ab + b².

In this case, a = √5 and b = 2.

(√5 - 2)² = (√5)² - 2(√5)(2) + (2)² = 5 - 4√5 + 4

So, the simplified expression is 9 - 4√5.

3. √3(2√3 + √12)

First, simplify the square root inside the parentheses:

√12 = √(4 * 3) = 2√3

Now, substitute this back into the expression:

√3(2√3 + 2√3)

Now, distribute the √3:

2√3 * √3 + 2√3 * 2√3

= 2 * 3 + 4 * 3

= 6 + 12

= 18

So, the simplified expression is 18.

4. 4√2 + √50 - √18

First, simplify the square roots:

√50 = √(25 * 2) = 5√2 √18 = √(9 * 2) = 3√2

Now, substitute these back into the expression:

4√2 + 5√2 - 3√2

Now, combine like terms:

(4√2 + 5√2) - 3√2 = 9√2 - 3√2

= 6√2

So, the simplified expression is 6√2.