Question

What is the value of the expression

Answer 1

Hi there! Hopefully this helps!

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The answer: $\frac{7}{9}$.

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$\sqrt[]{2}$ × $\frac{8\sqrt{2} }{3}$ ÷ 3 - 1

First, we express $\sqrt{2}$ × $(\frac{8\sqrt{2}}{3})$ ≈ 5.333333333 as a single fraction.

$\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} } - 1$  ≈ 0.777777778

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Now we express $\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} }$ ≈ 1.777777778 as a single fraction.

$\frac{\sqrt{2 \times 8\sqrt{2} } }{3 \times 3} - 1$  ≈ 0.777777778

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Multiply $\sqrt{2}$ ≈ 1.414213562 and $\sqrt{2}$ ≈ 1.414213562 to get 2.

$\frac{2 \times 8}{3 \times 3} - 1$ ≈ 0.777777778

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Multiply 2 and 8 to get 16.

$\frac{16}{3 \times 3} - 1$ ≈ 0.777777778

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Multiply 3 and 3 to get 9.

$\frac{16}{9} - 1$ ≈ 0.777777778

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Convert 1 to fraction $\frac{9}{9} = 1.$

$\frac{16}{9} - \frac{9}{9}$ ≈ 0.777777778

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Since $\frac{16}{9}$ ≈ 1.777777778 and $\frac{9}{9} = 1$ have the same denominator, subtract them by subtracting their numerators.

$\frac{16 - 9}{9}$

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Then you get................

$\frac{7}{9}$