simplify (sqrt(3)-1)/(sqrt(2)-1)

Let's reduce:

\frac{\sqrt{3} - 1}{\sqrt{2} - 1}

Multiply numerator and denominator by the conjugate

\sqrt{2} + 1

: (a+b)(a-b) = a²-b², here

{(\sqrt{2})}^{2} - 1

2 - 1

1

ⅰ

\frac{\sqrt{3} - 1}{\sqrt{2} - 1}

(\sqrt{3} - 1) \times (\sqrt{2} + 1)

(\sqrt{3} - 1) \times (\sqrt{2} + 1)

ⓘ Expand by multiplying each term inside the parentheses:

(\sqrt{3} - 1) \times (\sqrt{2} + 1)

\sqrt{3} \times \sqrt{2}

+ \sqrt{3} \times 1

- 1 \times \sqrt{2}

- 1 \times 1

\sqrt{3} \times \sqrt{2}

+ \sqrt{3} \times 1

- 1 \times \sqrt{2}

- 1 \times 1

ⓘ Powers with the same exponent are multiplied by multiplying the bases:

\sqrt{3} \times \sqrt{2}

\sqrt{3 \times 2}

■Multiplying by 1 changes nothing:

1 \times \sqrt{2}

\sqrt{2}

\sqrt{3 \times 2}

+ \sqrt{3}

- \sqrt{2}

- 1

ⅰ

3 \times 2

6

▶Simplified form:

\sqrt{6}

+ \sqrt{3}

- \sqrt{2}

- 1

The numeric value of:

\sqrt{6}

+ \sqrt{3}

- \sqrt{2}

- 1

is:

\approx 2.4495

+ \approx 1.7321

- \approx 1.4142

- 1

\approx 4.1815 - \approx 1.4142 - 1

\approx 2.7673 - 1

▷

\approx 1.7673