Question

evaluate the following
1⇒ 2√2 + 3√2
2⇒ 5√3 - 2√2 - 7√3 + 4√2
3⇒ 5√2 - √6 + √3 - 2√6 + 4√3 - 5√2
4⇒ (2 - √2)(2 + √2)
5⇒ (3 - √2)(3 - √3)
6⇒ (2 + √2)(3 - √3)
7⇒ 1/2+√3 + 1/2-√3

Answer 1

HEY MATE

HERE IS YOUR ANSWER.

Answer 2

$\huge\bold{Solutions}$

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(1). 2√2 + 3√2 = 5√2

(2). 5√3 - 2√2 - 7√3 + 4√2

= 5√3 - 7√3 - 2√2 + 4√2

= -2√3 -2√2

= -2(√3 + √2)

(3). 5√2 - √6 + √3 - 2√6 + 4√3 - 5√2

= 5√2 - 5√2 - √6 - 2√6 + √3 + 4√3

= 0 - 3√6 + 5√3

= -3√6 + 5√3

(4). (2 - √2)(2 + √2)

= (2)² - (√2)²

= 4 - 2

= 2

(5). (3 - √2)(3 - √3)

= 3(3) - 3(√3) - √2(3) - √2(√3)

= 9 - 3√3 - 3√2 - √6

(6). (2 + √2)(3 - √3)

= 2(3) - 2(√3) + √2(3) - √2(√3)

= 6 - 2√3 + 3√2 - √6

(7).

$= \frac{1}{2} + \sqrt{3} \: + \frac{1}{2} - \sqrt{3}$

$= \frac{1}{2} + \frac{1}{2} \: + \sqrt{3} \: - \sqrt{3}$

$= \frac{1 + 1}{2} + 0$

$= \frac{2}{2}$

= 1

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Hope it helps u Out☯️