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Identities for Irrational Numbers

Simplify i 3-...

Question

Simplify

(i) $(3 - \sqrt{11}) (3 + \sqrt{11})$

(ii) $(- 3 + \sqrt{5}) (- 3 - \sqrt{5})$

(iii) $(3 - \sqrt{3})^{2}$

(iv) $(\sqrt{5} - \sqrt{3})^{2}$

(v) $(5 + \sqrt{7}) (2 + \sqrt{5})$

(vi) $(\sqrt{5} - \sqrt{2}) (\sqrt{2} - \sqrt{3})$

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Similar questions

Q. Simplify
(i)

(3 - \sqrt{11}) (3 + \sqrt{11})

(- 3 + \sqrt{5}) (- 3 - \sqrt{5})

{(3 - \sqrt{3})}^{2}

{(\sqrt{5} - \sqrt{3})}^{2}

(5 + \sqrt{7}) (2 + \sqrt{5})

(\sqrt{5} - \sqrt{2}) (\sqrt{2} - \sqrt{3})

Q. Simplify:

(i)

(\sqrt{3} + \frac{1}{\sqrt{3}}) (\sqrt{3} - \frac{1}{\sqrt{3}})

(\sqrt[4]{6} - \sqrt[4]{5}) (\sqrt[4]{6} + \sqrt[4]{5}) (\sqrt[]{6} + \sqrt[]{5})

(\sqrt{5} + \sqrt{2}) (\sqrt{5} + 3 \sqrt{2})

2 \sqrt{x^{3}} \times x \sqrt[3]{a}

\sqrt[3]{2} \times \sqrt{5}

\sqrt{2} . \sqrt[3]{3} . \sqrt[4]{4}

\sqrt[6]{12} \div (\sqrt{3} \sqrt[3]{2})

\sqrt[4]{28} \div \sqrt[3]{7}

6 \sqrt[3]{25} \div \sqrt[2]{5}

\sqrt[6]{256} \div \sqrt[3]{2}

\sqrt{x^{6} y^{3}} \div \sqrt[3]{x^{2} y}

Q. Simplify

(i)

\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}

\frac{1}{\sqrt{3} + \sqrt{2}} - \frac{2}{\sqrt{5} - \sqrt{3}} - \frac{3}{\sqrt{2} - \sqrt{5}}

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

\frac{2 \sqrt{6}}{\sqrt{2} + \sqrt{3}} + \frac{6 \sqrt{2}}{\sqrt{6} + \sqrt{3}} - \frac{8 \sqrt{3}}{\sqrt{6} + \sqrt{2}}

Q. Simplify
(i)

10 \sqrt{2} - 2 \sqrt{2} + 4 \sqrt{32}

\sqrt{48} - 3 \sqrt{72} - \sqrt{27} + 5 \sqrt{18}

\sqrt[3]{16} + 8 \sqrt[3]{54} - \sqrt[3]{128}

.

Q. Simplify
(i)

(10 + \sqrt{3}) (2 + \sqrt{5})

(\sqrt{5} + \sqrt{3})^{2}

(\sqrt{13} - \sqrt{2}) (\sqrt{13} + \sqrt{12})

(8 + \sqrt{3}) (8 - \sqrt{3})

.

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