Poenostavite ta sqrt (9 ^ (16x ^ 2))?

Odgovor:

$\sqrt{9^{16 x^{2}}} = 9^{8 x^{2}} = 43, 046, 721^{x^{2}}$ $sqrt (9 ^ (16x ^ 2)) = 9 ^ (8x ^ 2) = 43,046,721 ^ (x ^ 2)$

(ob predpostavki, da želite samo primarni kvadratni koren)

Pojasnilo:

Od $b^{2 m} = {(b^{m})}^{2}$ $b ^ (2m) = (b ^ m) ^ 2$

$\sqrt{9^{16 x^{2}}} = \sqrt{{(9^{8 x^{2}})}^{2}}$ $sqrt (9 ^ (16x ^ 2)) = sqrt ((9 ^ (8x ^ 2)) ^ 2)$

$¯ v a (b e l a) (XXX) = 9^{8 x^{2}}$ $barva (bela) ("XXX") = 9 ^ (8x ^ 2)$

$¯ v a (b e l a) (XXX) = {(9^{8})}^{x^{2}}$ $barva (bela) ("XXX") = (9 ^ 8) ^ (x ^ 2)$

$¯ v a (b e l a) (XXX) = 43, 046, 721^{x^{2}}$ $barva (bela) ("XXX") = 43,046,721 ^ (x ^ 2)$

Odgovor:

$3^{16 x^{2}}$ $3 ^ (16x ^ 2)$ ali $9^{8 x^{2}}$ $9 ^ (8x ^ 2)$

Pojasnilo:

$\sqrt{9^{16 x^{2}}} = {(9^{16 x^{2}})}^{\frac{1}{2}} = 9^{(\frac{1}{2}) 16 x^{2}}$ $sqrt (9 ^ (16x ^ 2)) = (9 ^ (16x ^ 2)) ^ (1/2) = 9 ^ ((1/2) 16x ^ 2)$

$= {(9^{\frac{1}{2}})}^{16 x^{2}} = 3^{16 x^{2}}$ $= (9 ^ (1/2)) ^ (16x ^ 2) = 3 ^ (16x ^ 2)$ ALI $= 9^{(\frac{1}{2} \cdot 16) x^{2}} = 9^{8 x^{2}}$ $= 9 ^ ((1/2 * 16) x ^ 2) = 9 ^ (8x ^ 2)$

Odgovor:

$3^{16 x^{2}}$ $3 ^ (16x ^ 2)$

Pojasnilo:

Ta izraz lahko poenostavite z uporabo različnih lastnosti radikalov in eksponentov. Na primer, to veste

$\sqrt{x} = x^{\frac{1}{2}}$ $color (modra) (sqrt (x) = x ^ (1/2)) ""$ in $¯ v a (mod r a) ({(x^{a})}^{b} = x^{a \cdot b})$ $"" barva (modra) ((x ^ a) ^ b = x ^ (a * b))$

V tem primeru bi dobili

$\sqrt{9^{16 x^{2}}} = 9^{16 x^{2}}^(\frac{1}{2}) = 9^{16 x^{2} \cdot \frac{1}{2}} = 9^{8 x^{2}}$ $sqrt (9 ^ (16x ^ 2)) = 9 ^ (16x ^ 2) ^ (1/2) = 9 ^ (16x ^ 2 * 1/2) = 9 ^ (8x ^ 2)$

Ker to veš $9 = 3^{2}$ $9 = 3^2$ , lahko to prepišete kot

$9^{8 x^{2}} = {(3^{2})}^{8 x^{2}} = 3^{16 x^{2}}$ $9 ^ (8x ^ 2) = (3 ^ 2) ^ (8x ^ 2) = 3 ^ (16x ^ 2)$

Drug pristop, ki ga lahko uporabite, je

$\sqrt{9^{16 x^{2}}} = \sqrt{{(9^{8 x^{2}})}^{2}} = 9^{8 x^{2}} = 3^{16 x^{2}}$ $sqrt (9 ^ (16x ^ 2)) = sqrt ((9 ^ (8x ^ 2)) ^ 2) = 9 ^ (8x ^ 2) = 3 ^ (16x ^ 2)$

Lahko pa tudi uporabite

$\sqrt{9^{16 x^{2}}} = \sqrt{{(9^{x^{2}})}^{16}} = {(9^{x^{2}})}^{8} = {(3^{2})}^{x^{2}}^8 = 3^{16 x^{2}}$ $sqrt (9 ^ (16x ^ 2)) = sqrt ((9 ^ (x ^ 2)) ^ 16) = (9 ^ (x ^ 2)) ^ 8 = (3 ^ 2) ^ (x ^ 2) ^ 8 = 3 ^ (16x ^ 2)$

Kaj je (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt (3-) sqrt (5))?

2/7 vzamemo, A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5) -sqrt3) / (2sqrt3-sqrt5) = (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5-sqrt3) ) (2sqrt3 + sqrt5) ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15-5 + 2 * 3-sqrt15)) / ((2sqrt3)) ^ 2- (sqrt5) ^ 2) = (prekliči (2sqrt15) -5 + 2 * 3zaključi (-sqrt15) - prekliči (2sqrt15) -5 + 2 * 3 + prekliči (sqrt15)) / (12-5) = ( -10 + 12) / 7 = 2/7 Upoštevajte, da če je v imenovalcu (sqrt3 + sqrt (3 + sqrt5)) in (sqrt3 + sqrt (3-sqrt5)), bo odgovor spremenjen.

Kako poenostavite (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / ( (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?

Ogromno oblikovanje matematike ...> barva (modra) (((1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) ) / (sqrt (a + 1) / ((a-1) sqrt (a + 1) - (a + 1) sqrt (a-1))) = barva (rdeča) (((1 / sqrt (a- 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (a +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) = barva ( modro) ((((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a -1)))) / (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) = barva (rdeča) ((1 / sqr

Poenostavite izraz ?: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169))

1 Prva opomba: 1 / (sqrt (n + 1) + sqrt (n)) = (sqrt (n + 1) -sqrt (n)) / ((sqrt (n + 1) + sqrt (n)) ( sqrt (n + 1) -sqrt (n)) barva (bela) (1 / (sqrt (n + 1) + sqrt (n))) = (sqrt (n + 1) -sqrt (n)) / (( n + 1) -n) barva (bela) (1 / (sqrt (n + 1) + sqrt (n))) = sqrt (n + 1) -sqrt (n) Torej: 1 / (sqrt (144) + sqrt (145) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169)) = (sqrt (145) -sqrt (144)) + (sqrt (146) -sqrt (145)) + ... + (sqrt (169) -sqrt (168)) = sqrt (169) -sqrt (144) = 13-12 = 1