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What is the value of the expression?

What is the value of the expression?-example-1
User RisingSun
by
8.2k points

1 Answer

2 votes

Answer:

13/6

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

User JefferMC
by
8.0k points

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