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प्रश्न
Simplify of the following:
`root(3)4 xx root(3)16`
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उत्तर
We know that `root(n)a xx root(n)b = root(n)(ab)`.
We will use this property to simplify the expression `root(3)4 xx root(3)(16)`
`∴ root(3)(4) xx root(3)(16) = root(3)(64)`
`= root(3)(4^3)`
`= (4)^1`
= 4
Hence the value of the given expression is 4
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संबंधित प्रश्न
Simplify of the following:
`root(4)1250/root(4)2`
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt10 + sqrt15)/sqrt2`
`
Rationales the denominator and simplify:
`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
\[\sqrt{10} \times \sqrt{15}\] is equal to
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`(sqrt(10) - sqrt(5))/2`
If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.
