Question

simplify 12root 18+6root20-6root147+3root50+8root45​

Answer 1

Answer:

41√2 + 36√5 - 42√3.

Step-by-step explanation:

$12 \sqrt{18} + 6 \sqrt{20} - 6 \sqrt{147} + 3 \sqrt{50} \\ + 8 \sqrt{45} \\ \\ = 12 \sqrt{ {3}^{2} \times 2} + 6 \sqrt{ {2}^{2} \times 5} - 6 \sqrt{ {7}^{2} \times 3} \\ + 3 \sqrt{ {5}^{2} \times 2 } + 8 \sqrt{ {3}^{2} \times 5} \\ \\ = 12 \times 3 \sqrt{2} + 6 \times 2 \sqrt{5} - 6 \times 7 \sqrt{3} \\ + 3 \times 5 \sqrt{2} + 8 \times 3 \sqrt{5} \\ \\ = 36 \sqrt{2} + 12 \sqrt{5} - 42 \sqrt{3} + 15 \sqrt{2} \\ + 24 \sqrt{5} \\ \\ = 36 \sqrt{2} + 15 \sqrt{2} + 12 \sqrt{5} + 24 \sqrt{5} \\ - 42 \sqrt{3} \\ \\ \bf = 41 \sqrt{2} + 36 \sqrt{5} - 42 \sqrt{3}$

Answer 2

Answer:

41√2 + 36√5 - 42√3.

Step-by-step explanation:

\begin{lgathered}12 \sqrt{18} + 6 \sqrt{20} - 6 \sqrt{147} + 3 \sqrt{50} \\ + 8 \sqrt{45} \\ \\ = 12 \sqrt{ {3}^{2} \times 2} + 6 \sqrt{ {2}^{2} \times 5} - 6 \sqrt{ {7}^{2} \times 3} \\ + 3 \sqrt{ {5}^{2} \times 2 } + 8 \sqrt{ {3}^{2} \times 5} \\ \\ = 12 \times 3 \sqrt{2} + 6 \times 2 \sqrt{5} - 6 \times 7 \sqrt{3} \\ + 3 \times 5 \sqrt{2} + 8 \times 3 \sqrt{5} \\ \\ = 36 \sqrt{2} + 12 \sqrt{5} - 42 \sqrt{3} + 15 \sqrt{2} \\ + 24 \sqrt{5} \\ \\ = 36 \sqrt{2} + 15 \sqrt{2} + 12 \sqrt{5} + 24 \sqrt{5} \\ - 42 \sqrt{3} \\ \\ \bf = 41 \sqrt{2} + 36 \sqrt{5} - 42 \sqrt{3}\end{lgathered}

12

18

+6

20

−6

147

+3

50

+8

45

=12

3

2

×2

+6

2

2

×5

−6

7

2

×3

+3

5

2

×2

+8

3

2

×5

=12×3

2

+6×2

5

−6×7

3

+3×5

2

+8×3

5

=36

2

+12

5

−42

3

+15

2

+24

5

=36

2

+15

2

+12

5

+24

5

−42

3

=41

2

+36

5

−42

3