Question

Calculati: a) 3 radical 8 + 5 radical 18
b) radical 27 + 2 radical 12
c) radical 20 - 4 radical 45

Rationalizati: a) 5 supra 2 radical 5
b) 3 supra 4 radical 3
c) 9 supra 4 - radical 7
d) 3 supra 3 + radical 6


Calculati media aritmetica si media geometrica a numerelor: x= 2 radical 5 +3 radical 3
y= 2 radical 5 - 3 radical 2

Answer 1

Răspuns:

Explicație pas cu pas:

3√8 + 5√18 = 6√2 + 15√2 = 21√2

_________

√27 + 2√12 = 3√3 + 4√3 = 7√3

_________

√20 - 4√45 = 2√5 - 12√5 = -10√5

_______________

5/2√5 = 5√5/10 = √5/2

________

3/4√3 = 3√3/12 = √3/4

_______

9/(4 - √7) = 9(4 + √7)/(4 - √7)(4 + √7) = 9(4 + √7)/(16 - 7) = 9(4 + √7)/9 = 4 + √7

_______

3/(3 + √6) = 3(3 - √6)/(3 + √6)(3 - √6) = 3(3 - √6)/(9 - 6) = 3(3 - √6)/3 = 3 - √6

____________________

x = 2√5 + 3√3

y = 2√5 - 3√2

cred ca ai scris gresit la x. O sa consider x = 2√5 + 3√2

Ma = (2√5 + 3√2 + 2√5 - 3√2)/2 = 4√5/2 = 2√5

x*y = (2√5 + 3√2)(2√5 - 3√2) = 20 - 18 = 2

Mg = √x*y = √2