Question

What is the value of the expression?

Answer 1

Answer:

13/6

Step-by-step explanation:

1 Simplify  \sqrt{8}

8

​

  to  2\sqrt{2}2

2

​

.

\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

6×2

2

​

2

​

 

2

​

−(−

81

​

18

​

)

2 Simplify  6\times 2\sqrt{2}6×2

2

​

  to  12\sqrt{2}12

2

​

.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

12

2

​

2

​

 

2

​

−(−

81

​

18

​

)

3 Since 9\times 9=819×9=81, the square root of 8181 is 99.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})

12

2

​

2

​

 

2

​

−(−

9

18

​

)

4 Simplify  \frac{18}{9}

9

18

​

  to  22.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)

12

2

​

2

​

 

2

​

−(−2)

5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}

12

2

​

2

​

⋅

2

​

2

​

​

=

12×2

2

2

​

​

.

\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)

12×2

2

2

​

​

 

2

​

−(−2)

6 Simplify  12\times 212×2  to  2424.

\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)

24

2

2

​

​

 

2

​

−(−2)

7 Simplify  \frac{2\sqrt{2}}{24}

24

2

2

​

​

  to  \frac{\sqrt{2}}{12}

12

2

​

​

.

\frac{\sqrt{2}}{12}\sqrt{2}-(-2)

12

2

​

​

 

2

​

−(−2)

8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}

b

a

​

×c=

b

ac

​

.

\frac{\sqrt{2}\sqrt{2}}{12}-(-2)

12

2

​

 

2

​

​

−(−2)

9 Simplify  \sqrt{2}\sqrt{2}

2

​

 

2

​

  to  \sqrt{4}

4

​

.

\frac{\sqrt{4}}{12}-(-2)

12

4

​

​

−(−2)

10 Since 2\times 2=42×2=4, the square root of 44 is 22.

\frac{2}{12}-(-2)

12

2

​

−(−2)

11 Simplify  \frac{2}{12}

12

2

​

  to  \frac{1}{6}

6

1

​

.

\frac{1}{6}-(-2)

6

1

​

−(−2)

12 Remove parentheses.

\frac{1}{6}+2

6

1

​

+2

13 Simplify.

\frac{13}{6}

6

13

​

Done