Question

Please help to do this all questions ​

Answer 1

Step-by-step explanation:

a)

$5 \sqrt{2} - 13 \sqrt{2} + 10 \sqrt{2}$

$= \sqrt{2} (5 - 13 + 10)$

$= \sqrt{2} (2) = 2 \sqrt{2}$

b)

$\sqrt{32} + \sqrt{18} - 2 \sqrt{2}$

$= 3 \sqrt{2} + 4 \sqrt{2} - 2 \sqrt{2}$

$= \sqrt{2} (3 + 4 - 2)$

$= \sqrt{2} (5) = 5 \sqrt{2}$

c)

$( \sqrt{3} - \sqrt{2} ) \sqrt{3}$

$= ( \sqrt{3} \sqrt{3} ) - ( \sqrt{2} \sqrt{3} )$

$= 3 - \sqrt{6}$

d)

$\sqrt{5} ( \sqrt{5} - \sqrt{2} )$

$= ( \sqrt{5} \sqrt{5} ) - ( \sqrt{5} \sqrt{2} )$

$= 5 - \sqrt{10}$

e)

$\frac{4 \sqrt{50} }{ \sqrt{200} }$

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

f)

$2 \sqrt{6} \times \sqrt{3} \times \sqrt{2}$

$= 2 \sqrt{3 \times 2} \times \sqrt{3} \times \sqrt{2}$

$= 2 \times \sqrt{3} \times \sqrt{3} \times \sqrt{2} \times \sqrt{2}$

$= 2 \times 3 \times 2 = 12$

g) there's a formula that;

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

According to the problem ;

$(2 \sqrt{3} - \sqrt{5} )(2 \sqrt{3} + \sqrt{5} )$

$= {(2 \sqrt{3)} }^{2} - {( \sqrt{5} )}^{2}$

$= (4 \times 3) - 5 = 12 - 5 = 7$

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