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प्रश्न
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
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उत्तर
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7) = (4sqrt(4 xx 7) ÷ 3sqrt(7)) ÷ root(3)(7)`
= `((8sqrt(7))/(3sqrt(7))) ÷ (7)^(1/3)` ...`[∵ root(n)(a) = a^(1/n)]`
= `8/3 ÷ 7^(1/3)`
= `8/(3root(3)(7)`
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`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
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`1/(3 + sqrt2)`
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`30/(5sqrt3 - 3sqrt5)`
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`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
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Simplify:
`(1/27)^((-2)/3)`
