Question

Hi there
Simplify (√3-√2)(√3 +√2).
Use this to compute 1/(√3-√2) and 1/(√3 +√2) correct to two
decimal places.

Answer 1

Step-by-step explanation:

Lets first do the operation on $\bf (\sqrt3-\sqrt2)(\sqrt3+\sqrt2)\\ \bf In\ this,\ we\ will\ use,\ the\ formula,\ (a+b)(a-b)=a^2-b^2\\ \bf here,\ a=\sqrt3\ and\ b=\sqrt2\\ \bf Operaring\; (\sqrt3-\sqrt2)(\sqrt3-\sqrt2)\\ \bf \implies 3-2=1\\ \bf \therefore (\sqrt3-\sqrt2)=1$

First know, $\bf \sqrt3=1.732\ and \bf \sqrt2=1.414$

Now, we will complete our question

Now, we've to compute

$\bf \frac{1}{(\sqrt3-\sqrt2)}\\ \\ \implies \bf \frac{1}{1.732-1.414}\\ \\ \bf \frac{1}{0.318}\\ \\ \implies \bf 2.9256875366 \\ \therefore \bf \frac{1}{(\sqrt3-\sqrt2)}= 2.9256875366$

Similarly,

$\bf \frac{1}{(\sqrt3+\sqrt2)} \\ \\ \implies \bf \frac{1}{1.732+1.414} \\ \\ \implies \bf \frac{1}{3.146} \\ \\ \implies \bf 0.7606876616 \\ \therefore \bf \frac{1}{(\sqrt3+\sqrt2)}= 0.7606876616$