Question

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A challenge for moderators like Amansharma264, ItzFireBlaze etc ; current brainly stars like TheBrainliestUser, Fiza100 etc and current brainly blockbusters like BrainlyButterfliee, BrainlyWarrior20, itzheartcracer etc.

Other's could also give answerers but give the qualitied answer with full solution means have to include all steps. Qualitied answer!!!!!!!!

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Rationalize the denominators: ● 1/√2 ● 7/√15 ● 12-√5 ● 2/√2 ● 1/√7-√6 ● 1/√5+√2 ● 1/√7-2​

Answer 1

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

${\large{\pmb{\sf{\underline{Required \; Solutions...}}}}}$

We are asked to rationalize the denominators(with solutions):

${\bigstar}\: \: \small{\underline{\boxed{\sf{\dfrac{1}{\sqrt{2}} \: = \dfrac{\sqrt{2}}{2}}}}}$

${\bigstar}\: \: \small{\underline{\boxed{\sf{\dfrac{7}{\sqrt{15}} \: = \dfrac{7\sqrt{15}}{15}}}}}$

${\bigstar}\: \: \small{\underline{\boxed{\sf{\dfrac{12}{\sqrt{5}} \: = \dfrac{12\sqrt{15}}{5}}}}}$

${\bigstar}\: \: \small{\underline{\boxed{\sf{\dfrac{2}{\sqrt{2}} \: = \dfrac{2\sqrt{2}}{2}}}}}$

${\bigstar}\: \: \small{\underline{\boxed{\sf{\dfrac{1}{\sqrt{7} - \sqrt{6}} \: = \dfrac{\sqrt{7} + \sqrt{6}}{1}}}}}$

${\bigstar}\: \: \small{\underline{\boxed{\sf{\dfrac{1}{\sqrt{5} + \sqrt{2}} \: = \dfrac{\sqrt{5} - \sqrt{2}}{3}}}}}$

${\bigstar}\: \: \small{\underline{\boxed{\sf{\dfrac{1}{\sqrt{7} - {2}} \: = \dfrac{\sqrt{7} + {2}}{3}}}}}$

Explanation:

⠀⠀⠀⠀⠀⠀Solution part A

${\sf{\dashrightarrow \dfrac{1}{\sqrt{2}}}}$

${\sf{\dashrightarrow \dfrac{1}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}}}$

${\sf{\dashrightarrow \dfrac{\sqrt{2}}{(\sqrt{2})^{2}}}}$

${\sf{\dashrightarrow \dfrac{\sqrt{2}}{2}}}$

⠀⠀⠀⠀⠀⠀Solution part B

${\sf{\dashrightarrow \dfrac{7}{\sqrt{15}}}}$

${\sf{\dashrightarrow \dfrac{7}{\sqrt{15}} \times \dfrac{\sqrt{15}}{\sqrt{15}}}}$

${\sf{\dashrightarrow \dfrac{7\sqrt{15}}{(\sqrt{15})^{2}}}}$

${\sf{\dashrightarrow \dfrac{7\sqrt{15}}{15}}}$

⠀⠀⠀⠀⠀⠀Solution part C

${\sf{\dashrightarrow \dfrac{12}{\sqrt{5}}}}$

${\sf{\dashrightarrow \dfrac{12}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}}}$

${\sf{\dashrightarrow \dfrac{12\sqrt{5}}{(\sqrt{5})^{2}}}}$

${\sf{\dashrightarrow \dfrac{12\sqrt{15}}{5}}}$

⠀⠀⠀⠀⠀⠀Solution part D

${\sf{\dashrightarrow \dfrac{2}{\sqrt{2}}}}$

${\sf{\dashrightarrow \dfrac{2}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}}}$

${\sf{\dashrightarrow \dfrac{2\sqrt{2}}{(\sqrt{2})^{2}}}}$

${\sf{\dashrightarrow \dfrac{2\sqrt{2}}{2}}}$

⠀⠀⠀⠀⠀⠀Solution part E

${\sf{\dashrightarrow \dfrac{1}{\sqrt{7} - \sqrt{6}}}}$

${\sf{\dashrightarrow \dfrac{1}{\sqrt{7} - \sqrt{6}} \times \dfrac{\sqrt{7} + \sqrt{6}}{\sqrt{7} + \sqrt{6}}}}$

• (a-b) (a+b) = a² - b²

${\sf{\dashrightarrow \sqrt{7}^{2} - \sqrt{6}^{2}}}$

${\sf{\dashrightarrow \dfrac{\sqrt{7} + \sqrt{6}}{7 - 6}}}$

${\sf{\dashrightarrow \dfrac{\sqrt{7} + \sqrt{6}}{1}}}$

⠀⠀⠀⠀⠀⠀Solution part F

${\sf{\dashrightarrow \dfrac{1}{\sqrt{5} + \sqrt{2}}}}$

${\sf{\dashrightarrow \dfrac{1}{\sqrt{5} + \sqrt{2}} \times \dfrac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}}}$

• (a-b) (a+b) = a² - b²

${\sf{\dashrightarrow \sqrt{5}^{2} - \sqrt{2}^{2}}}$

${\sf{\dashrightarrow \dfrac{\sqrt{5} - \sqrt{2}}{5-2}}}$

${\sf{\dashrightarrow \dfrac{\sqrt{5} - \sqrt{2}}{3}}}$

⠀⠀⠀⠀⠀⠀Solution part G

${\sf{\dashrightarrow \dfrac{1}{\sqrt{7} - {2}}}}$

${\sf{\dashrightarrow \dfrac{1}{\sqrt{7} - {2}} \times \dfrac{\sqrt{7} + {2}}{\sqrt{7} + {2}}}}$

• (a-b) (a+b) = a² - b²

${\sf{\dashrightarrow \sqrt{7}^{2} - 2^{2}}}$

${\sf{\dashrightarrow 7-4}}$

${\sf{\dashrightarrow 3}}$

${\sf{\dashrightarrow \dfrac{\sqrt{7} + {2}}{3}}}$