Question

Simplify:

3 square root of 10 end root plus 7 square root of 15 end root minus 6 square root of 10 end root minus 4 square root of 15

A.)3 square root of 10 end root minus 3 square root of 15

B.) 3 square root of 15 end root minus 3 square root of 10

C.) 3 square root of 30 end root minus 3 square root of 20

D.) 3 square root of 20 end root minus 3 square root of 30

Answer 1

Simplify:

4 square root of 2 end root plus 7 square root of 2 end root minus 3 square root of 2

A.) 2 square root of 8

B.) 8 square root of 2

C.) 8 square root of 6

D.) 6 square root of 8

Answer 2

Simplify:

7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54

A.) 11 square root of 6 end root minus 7 square root of 12

B.) 11 square root of 3 end root minus 7 square root of 6

C.) negative 3 square root of 9

D.) 4 square root of 9

Answer 3

\[\color{blue}{ 4\sqrt{2} +7\sqrt{2} -3\sqrt{2} } \]\[\color{blue}{ \sqrt{2}~(4 +7-3) } \]\[\color{blue}{ \sqrt{2}~(8) } \]\[\color{blue}{ So,~~~~~~~~~~~~~~~~~8 \sqrt{2} } \]

Answer 4

Lets see the second problem.

\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\sqrt{48} -\sqrt{54}} \]

Answer 5

\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{red} { \sqrt{48} } -\sqrt{54}} \]\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{red} { \sqrt{16 \times 3} } -\sqrt{54}} \]\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{red} { \sqrt{16} \times \sqrt{3} } -\sqrt{54}} \]\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{red} { 4\sqrt{3} } -\sqrt{54}} \]

Answer 6

Thank you

Answer 7

I am not done.

Answer 8

oh sorry

Answer 9

\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{blue} { 4\sqrt{3} } -\sqrt{54}} \]\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{blue} { 4\sqrt{3} } -\color{red} { \sqrt{54} }} \]\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{blue} { 4\sqrt{3} } -\color{red} { \sqrt{9 \times 6} }}\]\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{blue} { 4\sqrt{3} } -\color{red} { \sqrt{9} \times \sqrt{6} }}\]\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{blue} { 4\sqrt{3} } -\color{red} { 3 \sqrt{6} }}\]

Answer 10

Now lets find the like terms, the problem now looks like,
\[\color{blue}{ 7\sqrt{3}- 4\sqrt{6}+\color{blue} { 4\sqrt{3} } -\color{blue} { 3 \sqrt{6} }}\]

Like terms are as follows:
\[\color{green}{ 7\sqrt{3} \color{purple} { -4 \sqrt{6} }+\color{green} { 4\sqrt{3} } \color{purple} { -3 \sqrt{6} }}\]
\[\color{green}{ 7\sqrt{3} +\color{green} { 4\sqrt{3} } \color{purple} { -4 \sqrt{6} } \color{purple} { -3 \sqrt{6} }}\]
\[\color{green}{ \color{green} { 11\sqrt{3} } \color{purple} { -7 \sqrt{6} } }\]

so you finally get,
\[\color{blue}{ \color{blue} { 11\sqrt{3} } \color{blue} { -7 \sqrt{6} } }\]

Answer 11

thank you