Question

1. restrangeti , dupa ce ati scos factorii de sub radical:
a. √18+√8-√32
b √45+√125+√20
c. √3+√27-√12+√48
d. √24-√54-6√6

2. Soateti factorii de sub radical , apoi calculati :
a (√18+√288)-(√98+√200)
b 4√18+5√108-2√72
c 3√162-5√12-4√75+2√50
d. -4√216+3√96-√54+2√600

Answer 1

Explicație pas cu pas:

1.

""""

a) √18 + √8 - √32 =

√(2•3^2) + √(2^3) - √(2^5) =

3√2 + 2√2 - 4√2 =

√2 • (3 + 2 - 4) =

√2 • 1 =

√2

"""""

b) √45 + √125 + √20 =

√(3^2•5) + √(5^3) + √(2^2•5) =

3√5 + 5√5 + 2√5 =

√5 • (3 + 5 + 2) =

√5 • 10 =

10√5

"""""""

c) √3 + √27 - √12 + √48 =

√3 + √(3^3) - √(2^2•3) + √(2^4•3) =

√3 + 3√3 - 2√3 + 4√3 =

√3 • (1 + 3 - 2 + 4) =

√3 • 6 =

6√3

""""""

d) √24 - √54 - 6√6 =

√(2^3•3) - √(2•3^3) - 6√6 =

2√(2•3) - 3√(2•3) - 6√6 =

2√6 - 3√6 - 6√6 =

√6 • (2 - 3 - 6) =

√6 • (-7) =

- 7√6

"""""""""

2.

""""

a) (√18 + √288) - (√98 + √200) =

√(2•3^2) + √(2^5•3^2) - √(2•7^2) - √(2^3•5^2) =

3√2 + 4•3√2 - 7√2 - 2•5√2 =

3√2 + 12√2 - 7√2 - 10√2 =

√2 • (3 + 12 - 7 - 10) =

√2 • (-2) =

-2√2

""""""""

b) 4√18 + 5√108 - 2√72 =

4√(2•3^2) + 5√(2^2•3^3) - 2√(2^3•3^2) =

4 • 3√2 + 5• 2 • 3√3 - 2 • 2 • 3√2 =

12√2 + 30√3 - 12√2 =

30√3

""""""""

c) 3√162 - 5√12 - 4√75 + 2√50 =

3√(2•3^4) - 5√2^2•3) - 4√(3•5^2) - 2√(2•5^2) =

3 • 9√2 - 5 • 2√3 - 4 • 5√3 - 2 • 5√2 =

27√2 - 10√3 - 20√3 - 10√2 =

√2 • (27 - 10) - √3 • (10 + 20 ) =

√2 • 17 - √3 • 30 =

17√2 - 30√3

""""""""""""""""""

d) -4√216 + 3√96 - √54 + 2√600 =

-4√(2^3•3^3) + 3√(2^5•3) - √(2•3^3) + 2√(2^3•3•5^2) =

-4 • 2 • 3√(2•3) + 3 • 4√(2•3) - 3√(2•3) + 2 • 2 • 5√(2•3) =

- 24√6 + 12√6 - 3√6 + 20√6 =

√6 • ( - 24 + 12 - 3 + 20) =

√6 • 5 =

5√6

"""""""

^ = simbol folosit ptr ridicarea la putere

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