2 Improved the English and the title

# How todo I simplify theseexpressions with square root of the numberroots?

For example:I want

$$\left\{\frac{1}{1+\sqrt{2}-\sqrt{3}},\sqrt{5-2 \sqrt{6}},\sqrt{4+\sqrt{15}}\right\}$$

canto be simplifysimplified to

$$\left\{\frac{1}{4} \left(2+\sqrt{2}+\sqrt{6}\right), \sqrt{3}-\sqrt{2}, \frac{1}{2} \left(\sqrt{6}+\sqrt{10}\right)\right\}$$

But I can'thaven't been able to get thethat result with Mathematica.How How could I get it?

# How to simplify these square root of the number?

For example:

$$\left\{\frac{1}{1+\sqrt{2}-\sqrt{3}},\sqrt{5-2 \sqrt{6}},\sqrt{4+\sqrt{15}}\right\}$$

can be simplify to

$$\left\{\frac{1}{4} \left(2+\sqrt{2}+\sqrt{6}\right), \sqrt{3}-\sqrt{2}, \frac{1}{2} \left(\sqrt{6}+\sqrt{10}\right)\right\}$$

But I can't get the result with Mathematica.How?

# How do I simplify expressions with square roots?

I want

$$\left\{\frac{1}{1+\sqrt{2}-\sqrt{3}},\sqrt{5-2 \sqrt{6}},\sqrt{4+\sqrt{15}}\right\}$$

to be simplified to

$$\left\{\frac{1}{4} \left(2+\sqrt{2}+\sqrt{6}\right), \sqrt{3}-\sqrt{2}, \frac{1}{2} \left(\sqrt{6}+\sqrt{10}\right)\right\}$$

But I haven't been able to get that result with Mathematica. How could I get it?

1

# How to simplify these square root of the number?

For example:

$$\left\{\frac{1}{1+\sqrt{2}-\sqrt{3}},\sqrt{5-2 \sqrt{6}},\sqrt{4+\sqrt{15}}\right\}$$

can be simplify to

$$\left\{\frac{1}{4} \left(2+\sqrt{2}+\sqrt{6}\right), \sqrt{3}-\sqrt{2}, \frac{1}{2} \left(\sqrt{6}+\sqrt{10}\right)\right\}$$

But I can't get the result with Mathematica.How?