Question

if under root 2 equals to 1.414 to find value of under root under root 2 minus one upon under root 2 + 1

Answer 1

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Answer 2

Answer:

The value of $\frac{\sqrt{2}-1}{\sqrt{2}+1}$ =$0.172$

Explanation:

Given ,

√2 = 1.414 ---(1)

Value of $\frac{\sqrt{2}-1}{\sqrt{2}+1}$

Rationalising the denominator we get,

=$\frac{(\sqrt{2}-1)(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}$

= $\frac{(\sqrt{2}-1)^{2}}{(\sqrt{2})^{2}-1^{2})}$

/* By algebraic identity:

(a+b)(a-b) = a²-b² */

= $\frac{(\sqrt{2})^{2}-2\times \sqrt{2}\times 1+1^{2}}{(2-1)}$

/* By algebraic identity:

(a-b)² = a²-2ab+b² */

= $\frac{2-2\sqrt{2}+1}{1}$

= $3-2\sqrt{2}$

= $3-2\times1.414$

/* From (1) */

= $3-2.828$

= $0.172$

Therefore,

The value of $\frac{\sqrt{2}-1}{\sqrt{2}+1}$ =$0.172$

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